Oiling the bore is a tricky business, though once the technique is mastered it's quite simple. This page is divided into three sections, you can skip the first section if you're confident you really want to oil the bore! It's a relatively large document, so I'd advise you save it as an html document and read it at your leisure.

Section One covers the theory, and discusses the pros and cons of oiling the bore.
Section Two describes the materials required.
Section Three describes the technique.

Section One: The Theory.

Wood is a living material. Long after the tree has been felled, the wood continues to move and breathe. If left to its own devices, wood will eventually break down ( with the aid of moulds and fungi ) in a process we know as ‘rotting’.

Some woods are more resilient than others, and thus we choose these woods to make objects that will survive for long periods of time in extreme environments.
The Blackwoods ( a large family of dense, hard woods ) are most commonly used for woodwind instruments - with a close grain structure and good stability they lend themselves well to the manufacturing processes needed to make a complex turned and bored structure such as the body of a clarinet.

But even these very dense woods need care and attention if they are to survive in an environment that is usually wet and humid.
All woods contain oils, natural oils produced by the tree to protect and preserve the cellular structure of the wood itself, but as soon as the tree is felled the production of this life-giving oil stops. From then on the wood has to rely on the oils stored in its structure at the time it was cut down.
Most woods do pretty well, take a look at the vast catalogue of antique furniture that exists today - but when it comes to musical instruments there are other considerations. Day in, day out, the wood is subjected to an influx of warm, moisture laden air - not to mention the assorted acids, sugars and fats present in your breath. Hardly conducive to preservation!

When wood loses its natural oils several things happen. The wood dries out - and if it remained dry then perhaps there would not be too many problems, but once the oils have gone it leaves the structure dry and sponge-like - and thirsty!
What happens next is that the wood begins to absorb moisture from the atmosphere. This moisture provides the perfect breeding ground for the moulds and fungi whose job it is to break down the wood so that our planet is not littered with dead bits of wood!

The lack of oil has another effect. Water tends to be more volatile than oil - that’s to say that if you placed a drop of water beside a drop of oil on a plate of glass it’s the water that evaporates first. And this happens within the body of a wooden instrument too.
This constant cycle of evaporation and replenishment causes the wood to expand and contract. An excess of moisture or dryness will result in a greater movement of the wood when it dries or becomes wet. What then happens is the wood splits.
This is all part of the natural process of rotting. Fine for an old log on the forest floor - but not very nice for your expensive clarinet!
So if the oils in the wood were kept ‘topped up’ it follows that these environmental swings can be minimised, and the natural processes of rotting can be held at bay for a great many years.

There are drawbacks though.
In life, the tree carefully regulates the oils in its structure - in the same way our bodies regulate the sugars in our bloodstream. Too much or too little can have devastating consequences.
So when we replace the oil in the wood by artificial means we may well be guilty of ‘overloading’ the wood with oil. What this does is lock moisture deep within the grain of the wood. Under normal circumstances the water can move freely in and out of the pores - in other words the wood breathes. But if so much oil has been absorbed by the wood then it is possible that this water may not be able to escape, and in the expansion that inevitably follows the wood may split.
Having said all that you'd really have to go some to overload the wood with oil!

These then are the basic pros and cons.
There is one other ‘con’ though, and that relates to the technique itself. Applying oil to the bore of an instrument carries the risk that some of it will get onto the pads and keys of the instrument. Pads are tricky things at the best of times with regards to stickiness - so it’s obvious that any oil that gets onto these pads really isn't going to help at all.

It is here that I must state my personal and professional reasons for advocating the oiling of the bore.
The bulk of my work for the last ten years has been the restoration of period woodwind instruments. I have had to restore instruments that go back to the 15th century, made in a variety of materials. Perhaps the most common restoration work involves the rejuvenation of 18th and 19th century flutes and clarinets, typically made in Boxwood, Cocabola and Rosewoods.
It’s very common to find that the wood is bone dry - devoid of both water and oil. This makes the wood brittle, and prone to chipping. Rather more seriously it makes the wood extremely susceptible to humidity - so much so that tenon joints can lock solid on humid days, and fall free on dry days.

When a joint locks it exerts considerable pressure on the socket - which is why splits and cracks are a common sight on old instruments like these. It’s really quite something to see when a drop of water is placed on the bore of one of these ancient instruments - it soaks into the wood in no time at all, and any attempt to play such an instrument could do untold damage as the wood would absorb all the moisture it could get!
But with careful and patient oiling the wood can be revived and stabilised.

There's another good reason for oiling the bore. Many old clarinets that haven't seen a lick of bore oil for years often have a dull white coating on the bore. This is essentially scale - much the same as you might find in your kettle. It serves no purpose in a kettle, so you can imagine how useless it is in the bore of an instrument! It blocks the pores of the wood, fouls up the tone holes and affects the tone - and the tuning in extreme cases.
If this has happened to your instrument then you will need to have this scale removed - it's pretty impervious to bore oil.

The worst example I have seen of the wood drying out was a Serpent that was given to me for ‘restoration’.
A Serpent is a ‘double S’ shaped instrument, made of wood wrapped in leather but blown with a brass mouthpiece - this instrument had dried out centuries ago and was little more than a leather shell enclosing a pile of dust. Had the instrument been oiled down the years then it would probably have been in respectable condition - but without the protection of oil, time and nature had taken its course.
The only way to preserve the instrument was to inject the bore with a resin to bond the dust together. The instrument is now on display in a museum.
Obviously, such degradation is an extreme - but even a clarinet of some ten years of age may exhibit slight rotting, particularly on the bevels of the tone holes.

Wood has a ‘feel’ to it. Over the years, if you handle wood on a day-to-day basis, you get to understand it - and there’s many a time when I pick up an old clarinet and note that it doesn't ‘feel’ right. It feels too light. Too dead. Too cold. Oil brings the wood back to life, restores a sense of ‘body’ to the instrument - and best of all it makes it playable again without risk of damaging the wood.
If I felt that oiling the bore damaged the instruments entrusted to my care then I wouldn't do it - but until I have positive proof that oiling is detrimental then shall continue to advocate the process as a part of the care regime for woodwind instruments.

Section Two: The Materials:

It is not economically viable ( as far as I know! ) to extract natural oils from wood - it would destroy the wood, which defeats the object of cutting the tree down in the first place - so a substitute must be found, and ideally the oil must closely match the properties of the natural oil.

Vegetable oils are the closest match, but not all such oils are suitable. Some have certain properties that render them useless for our purposes.
Linseed oil is one such example. It is a ‘drying oil’ - which means that if you were to place a drop on a sheet of glass and leave it for a time it would harden into a resinous blob. Imagine that on the bore of your instrument!
Over the years the layers would build up, closing up the diameter of the bore and blocking the pores of the wood.
I cannot stress this strongly enough - Linseed oil MUST NOT be used. Walnut oil too is a drying oil.

There are two oils in common use for our purposes: Groundnut ( or peanut ) oil and Sweet Almond oil.
I used to recommend Lemon oil, but it seems that standards vary as to the composition of this oil - with some brands containing mineral oils and spirits. In some cases this oil can react with existing oils to form a greasy skin. Because there's no 'standard' for this oil I can't be certain you'll buy the right stuff - so it's off the list!
You can also buy Bore Oil from most music stores - but these can often be mineral based oils, which are nowhere near as good for the wood. Mineral oils will have a warning on the bottle saying ‘do not ingest’! Also, you may not know what additives commercial bore oils contain.
If you are allergic to nut products then seek medical advice before using Groundnut or Sweet Almond oil. Either of these may be purchased from most general food stores. I use Groundnut oil.

There has been some debate as to the risk of such oils going rancid. In theory all vegetable based oils will break down over time - but this assumes a quantity of oil left standing for a considerable amount of time. I have never found this to be a problem once the oil is applied to the bore - but you'd be well advised to ensure you use fresh oil in the first place. Choosing an oil like groundnut makes good sense in that it's a culinary oil...you can use it in the kitchen, thus ensuring a regular turnover of fresh oil.

Section Three: The Technique:

There are several methods of oiling the bore - but the one I am going to describe is, I feel, the safest for players who are oiling an instrument that has not been stripped down.

What you will need:

Your oil: You can decant it into a small bottle and mix in a little methylated spirits ( wood alcohol ) in the approximate ratio of seven parts oil, one part meths. Shake very well. This helps to thin the oil slightly, and disinfects the bore.

Clean up stuff: A few sheets of tissue or kitchen roll - to wipe off excess oil - and perhaps some lighter fluid and pipe cleaners, in case any of the pads get contaminated with oil.

An applicator: There are many alternatives. Given that I most often work with stripped down instruments I tend to favour an old clarinet 'Pad-Saver'.
( Incidentally - whilst I think these are brilliant for metal bodied instrument, I tend not to advise their use on wooden instruments as they may soak up the oil from the bore as well as the water - not what we want! ).
For maintenance 'in the home' I feel that using one of these could end up being rather messy! Alternatively you could use an old clarinet mop - one of those brush things on a length of twisted wire.
The problem here is that the filaments of the brush may run into the tone holes whilst you're oiling the bore - and you then run the risk of fouling the pads. If you prefer to use one of these then go for the denser variety - the ones that look like a roll of wool.

In this instance I'll show you how to make use of a oiling rod.
Essentially it's just a thin rod, about a foot long, with a slot cut into the top. A flute cleaning rod is ideal. Get a wooden one if at all possible - metal ones are fine, but you will need to exercise a little more care in use. You may well find your local music store sells a similar rod in plastic, for use with recorders. These are ideal.

You will also need a length of rag - about three inches wide, and a foot long. It has to be reasonably thick - an old, thick cotton bedsheet is ideal.
In any event, it ought not to be too fluffy, you don't want to coat the bore with bits of old sheet!

You'll need to wrap this strip around your rod. Simple enough, but you have to ensure two things - 1: that the tip of the rod is covered ( not so critical with a wooden rod ) and 2: that the cloth will not unwind. If it does so it may get wedged into the bore.
Start by threading a corner of the cloth through the slot like so...

Now roll the rod over into the cloth....

To protect the tip of the rod fold the top of the cloth down over it...

Now continue to roll the rod, feeding the cloth tightly down the rod as you go...

And you should end up with this...

The reason I specified strip of cloth about a foot long is that you'll now be able to keep hold of the end of it as you use the stick to oil the bore. This'll prevent the cloth coming loose.

This is what you do:
The object is to place a small quantity of the oil onto the bore of the instrument. The skill lies in not getting too much oil on the bore - or you risk fouling the pads. If you are using the Oil/Meths mixture, give it a good shake up first to combine the ingredients. What you now need to do is apply some oil to your applicator. Do not ‘dunk’ it in - you hardly need any oil at all - just dribble a little oil into the cup of your hand. Put the head of the applicator in the hand, clasp it and work it back and forth through your fist.
What you are trying to do is spread the oil evenly throughout the applicator and gauge whether you have too much oil. Perhaps the best way to ascertain the right amount of oil is to test the applicator on the barrel - where there are no keys present.

The applicator is inserted into the bore of the barrel - slowly and with a twisting motion. Take care to twist it in the same direction as the cloth was wound on...otherwise it may unwrap and lodge in the bore. Work it back and forth - gently. Examine the bore of the barrel - you are aiming to just dampen the bore evenly. Any obvious drips and runs mean you have far too much oil on the applicator. Run it through a kitchen towel to remove the excess oil - or work it out on the exterior of the barrel, or have a go at the bell! It is very important that you gauge the amount of oil on the applicator carefully - the aim is to smear the oil on, not slosh it. Then do the bell. Again, as this has no keys you can’t do any harm if you have too much oil on the applicator. Once you're sure you have the right balance of oil you can proceed to the main joints. Wash or wipe your hands first to avoid getting oil on the keywork.

Now the hard part. Start with the lower joint. Very carefully insert the applicator into the bottom joint from the lower end ( the bell end ). Don't apply too much downward pressure - the applicator ought to be a loose fit in the bore, and if you press it down onto the bore you run the risk of forcing excess oil out. Keep a very careful eye on the lowest tone hole. As the applicator passes the tone hole the edges of the hole might force oil out of the applicator. If oil runs into the tone hole then you could be in trouble. Keep the instrument level, with the keys uppermost, so that if any oil does dribble it won’t head straight for the pads.
Push the applicator all the way in. If it feels too tight, withdraw and wrap the cloth tighter. Repeat this a number of times, twisting the applicator round a little each time so that you cover the entire surface of the bore.

Tricky, isn't it?! The golden rule is to use as little oil as possible. Better to have to push the applicator in half a dozen times than risk it oozing oil everywhere. You'll be surprised at how 'dry' the applicator appears at first - and yet it also surprising just how much oil it can hold, which you usually find out too late!

Once you’re happy with the oil job - leave the clarinet to stand for an hour or so.

After an hour or so, inspect the clarinet. You should find that the oil has been absorbed into the two main joints. Excess oil in the bore can be cleaned out by threading a clean piece of cloth on the rod and repeating the above directions, but without any oil. Clean up the bell and the barrel, and check the tenon sockets for any excess oil.

If you've got the odd dribble onto the pads ( naughty! ) you can clean it off with a pipe cleaner bent double, soaked with a little lighter fluid. Any oil that gets onto the body will not do any harm, simply wipe it off with kitchen towel. If you so wish you can wipe a little oil onto the exterior of the instrument - but watch the keys and pads!

And that’s about it really.
As for how often you need to oil the bore - well, it depends on how often you play, how ‘wet’ a player you are, and what your local climate is like. Hot and damp places will mean there is more moisture in the atmosphere, so oiling will need to be done more frequently. Similarly hot and dry areas will tend to desiccate the wood.
If you’re a hardened pro then you might want to oil the bore every four months or so - a student will only need to oil once a year.

Bear in mind that it’s unlikely your instrument will fall apart if you miss out an oiling or two - it’s really a preventative and preservative technique. If your instrument is very old and hasn't been oiled for many years then you may need to oil it VERY lightly once a week for a month or so. Don't try to do it all at once - the stresses it can impose on the wood may lead to it splitting! New instruments will not need oiling in the first year - in fact you'll probably find that your pads get discoloured as the wood's natural oils leach out!
Bear in mind that some manufacturers do not recommend oiling the bore - and if you do so during your warranty period you may invalidate it!! It's up to you to weigh up the pros and cons as to whether you oil or not. Above all - remember, use as little oil as is possible, and take your time.