Bow basics
The bow is the of massive importance to the sound you get from your violin unless you are only ever going to pluck it! Different schools, approaches and styles suggest different ideas, some of which are quite conflicting, here is a general purpose guide to get you started.
Make sure you dust the rosin dust off your bow, violin and strings every time you finish playing, as excessive build-up of oxidised rosin can be bad for tone production.
Hair & Rosin
In order to make the bow work at all you need to have rosin on it (a small block of either orange or black material, which bears a passing resemblance to a large boiled sweet). Rosin increases the friction between the hair and the string, without it you bow would have a similar effect as rubbing your violin with a jumper.
Generally you should apply rosin to the bow every time before you play. 3-5 rubs of the rosin block along the full length of the hair should do it, or some people find it easier to go along applying it a few inches at a time until they reach the far end.
Not enough rosin and your violin will not sound properly, and you may feel areas that seem to slide across more easily. Too much rosin and you will end up standing in a dust cloud!
New bows may not have had any rosin applied so may need a lot more than this to get them started, equally new blocks of rosin are often slightly shinier and again need a bit more use to deliver dependable results.
It is almost impossible to say exactly how much rosin to use each time as it depends on so many factors, such as how much the instrument was played last time, how long ago, how loudly, the moisture of the air and so on. Gradually over time you will develop more experience and judgement. It is often better to err slightly on the side of caution as it is always possible to put more on.
Once you have got your bow rosined try to avoid touching the hair, as it not only rubs the rosin off but gets you all sticky as it comes in contact with sweat from your hands/nose/ears etc.
Bow Tension
The bow has a screw on it to enable you to tension it up to play on, and then release it once you have stopped so as not to warp the stick.
To play the bow should be done up so that the distance between the hair and the distance between the hair and the stick halfway down the bow is roughly equal to that of the thickness of the stick. Some styles call for more tension, some less, however if you bow gets to look straight rather than concave it it too tight and will not sit into the string properly.
Always undo the bow by a few turns when you finish playing so that the hair and stick are not under tension while in the case.
Ed Wright's Blog 