First and foremost, trackdays are about having fun and driving you car in a way that you can't on the road. It is not racing!
On your first day DO NOT try to be a trackday hero straight away, take your time and build up your pace. If someone is behind you lap after lap then you are holding them up, get out the way.
You will learn far more from following faster drivers, than by forcing them to wait behind you. Please also pull over to let them pass as early as possible, do not wait until a faster car is right on your rear bumper, or entering the braking zone before you (indicate and) pull over to let them pass.
At the same time do not drive aggressively behind another driver, give them time to move over. If they don't, come in and have a word with a marshall rather than lose your temper. Red mist on the track is a bad idea.
Passing is only allowed on the straights with the consent of the driver in front. Correct method is for the driver to recognise a faster car in their mirror, indicate right and pull offline (Overtaking rules may be different on some tracks but this is the general rule) lift off slightly until the car is passed and rejoin the correct racing line.
All this will be explained at the briefing, all drivers must attend this. The organisors will explain of the rules, flags etc. If anything is unclear or you are unsure do not be afraid to ask questions, they will be happy to help.
Most trackdays are open pit lane which means you can go on track whenever your want (at the instruction of the pit lane marshalls) and stay out as long as you want. Total numbers on track are limited at any one time but on open pit days it is rare to have to queue to join the track.
There are also sessioned days, usually limited to 20 mins at a time and divided into groups based on experience.
Flags
Please ensure that before entering onto the circuit that you are familiar with the following flag signals, as this is the marshalls only form of communicating with whilst you are on the circuit.
Red Danger
Session has been stopped. Check your mirrors, slow down immediately and proceed to the pits exercising extreme caution.
Yellow Slow Down
Slow down, do not overtake and be prepared to stop. A green flag may be shown when the danger is passed.
Blue Move Over
A faster car is stuck behind you and cannot pass.
Please move over to the right of the track as quickly as possible to permit the faster car to pass. The faster car may be slower in a straight line, so you may have to lift off briefly. Repeated blue flags may result in you being removed from the circuit.
Chequered Session Ends
Complete the end of the current lap and
return safely to the pits.
Black Return to Pits
Your car or driving is a danger to other participants. Please return to the pits immediately for further information.
Tyres
Tyres, you could completely wreck a brand new set in a day if you tried hard enough and you were a large ginger ape, but for most people provided you still have a few mill of legal tread on them they will still be fine at the end of the day. What you tend to find is the front left will get the heaviest wear on the outside shoulder (on clockwise circuits which most are). However you only tend to notice it after a few trackdays on the same set. Most folk new to trackdays should not really see much wear at all, although over driving the car and being ragged will increase wear. Buy a tyre pressure gauge and check the pressures after every session on track. The pressure will go up with the heat, especially on the heavily loaded tyres. You will kill your tyres unless you lower the pressure. Generally most people run a few psi lower than road levels.
Heavier cars will see more tyre wear then lightweight trackcars.
Some regular trackdayers buy a spare set of wheels to fit track tyres too, to avoid killing their road tyres.
Brakes
Brakes, make sure you have plenty left on the pads, the OEM are pretty good and will last for a good few trackdays. Make sure your fluid is topped up. If it is old or has been boiled at any time get it changed before tracking it. When on track, if you feel the peddle start to go soft come in immediately! Do not think you can squeeze another lap in as thats a classic noob trackday error and one of the most common causes of trackdays incidents, the brake pedal can go to the floor and you suddenly lose all braking if you ignore the warnings.
You may want to do a cool down lap to help the brakes, remember to keep well offline and watch your mirrors
Tip: When braking, do not follow the car in front to closely. The may have vastly different braking abilities than you which could result in you ploughing into the back of them or visiting a tyre wall.
Insurance
You can get trackday insurance via Competition Car Insurance you can expect to pay £10 for every £1k value of the car ie £150 per day for £15,000 car. The excess tends to be huge so it only really covers you for write offs which are very, very rare on track. What you can do is part insure it for a few £k which lowers the excess and covers you for minor prangs, which the majority of trackday incidents are.Worth checking if your insurance company provides trackday insurance, some provide full cover for a reasonable cost.
Remember, trackday insurance only covers you for your own car. If you drive into someone else their car is not covered, you had better hope their car has it's own insurance or the owner is very easy going!
Cost
Trackdays are not cheap, if you are worried about the cost here is a breakdown of what it's going to be.
You can expect to pay around £80-£250 for a full day session depending on time of year and track.
A full day will probably use up about 2-4 tanks of petrol, £100-£200
Brake pads should see at least half a dozen track days. I usually equate this to roughly £25 per day
Tyres should be good for a few trackdays, as mentioned they wear unevenly so you should keep an eye on them, again I would budget £50 per day for tyres.
Instruction
Most circuits and trackdays will have some on hand either free of charge or for a small fee. They will be able to help you out a lot with lines, braking points etc.
Never underestimate the value of trackday instruction, even the very best will listen to local knowledge. Even if you think you are doing well you are guaranteed that an instructor will still take seconds off your laptime.
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Oil and fuel
Make sure the oil is topped up and take a spare litre with you and continue to check it throughout the day.
Take a spare jerry can of fuel, I get fuel starvation if I run it too low. Not often a problem but remember to check it, its easy to forget when having fun. If you run out on track you will look like a plank and everyone will be pissed off at you for causing an unnecessary red flag.
General advice-
• Remove everything from boot
• Remove everything from inside car! I have been in a car when someone found a plastic bottle under their brake peddle approaching a heavy braking zone. I found it hilarious, the driver not so.
• Take it easy and build up your speed, classic error is to go straight off at the first corner.
• Check your mirrors for faster traffic coming up behind, holding them up gets frustrating but as long as you move over generally etiquette is good and they will give you plenty of space.
• Don't feel you have to jump out the way as soon as you see them, often those new to it feel that all they are doing is constantly moving over. Trick is to get into the habit of lifting off as early as possible after a corner NOT at the end of the straight. That way both cars lose the least time.
• Just when you think you have the hang of it and are getting quite good, come in to the pits because you're not. That might sound patronising but its sound advice. Its later in the day when sometimes confidence goes overboard and ambition overtakes talent. Some big offs can happen that way so always keep the sensible head on.
• If you go off don't panic. There are usually gravel traps and plenty of run off area, avoid going into gravel traps sideways, the car can dig into the gravel and roll! If you do take a trip through the scenery and kitty litter it is probably best coming into the pit to check the car, remove any mud or loose stones. DO NOT THROW THE STONES OUT OF THE CAR ON TRACK. At 100mph they turn into bullets will greatly upset your fellow trackdayers.
• If the car breaks down on track pull well off the racing line into the infield and get out of the car and over a tyre wall as quick as you can. The marshals will red flag the session so your car can be recovered. DO NOT attempt to work on your car during a live session.
• Remember don't put the handbrake on in the pits, you will boil your fluid. leave it in gear or chock the wheels.
• Leave a decent amount of time between session for the car to cool, 15-20mins should be fine. If you boil your brake fluid you will be waiting up to an hour for it to cool so that's another reason for no overdoing it on session lengths. I would suggest 8-10 laps to begin with.
• As well as fuel for the car you will need fuel for you
Trackdays can be hot and hard work, make sure you drink plenty of fluids and eat something. Done myself when getting carried away and not fed myself. You will find your concentration going and you don't want that on track.• Being smooth generally equals being fast, if you are throwing the car around you might look spectacular but you won't be quick.
• To get on track you car should be road legal and well maintained. You will need a helmet, your can use your own or most tracks will have some available for hire.
• Wear long sleeved top and trousers as some circuits require this for insurance reasons.
• Filming is allowed but make sure all camera equipment is well secured and can't fly about in the event of an off.
• Timing is not allowed is it invalidates the circuits insurance for trackdays, if you are caught timing your laps you may be told to leave!
• You are responsible for any passengers, make sure they have signed on for passenger laps and have attended the briefing.
• Do not speed in the pit lane.
• You may have to show your drivers license so have it with you.
• Have fun.
Spot on, great post! 
I should have kepy that Oasis juice bottle that came from nowhere!