The first rule of driving in Thailand is: Don't!
The second rule is: Don't!
The most incredible thing about driving in Thailand is that a people who are so lovely, friendly and forgiving turn into complete monsters when sitting in a car or complete idiots when sitting on a motorbike.
Actually driving in Thailand isn't quite so bad as its reputation would have you believe, but it still is not to be undertaken by the faint of heart.
Things to Remember
Drive on the left. Although others seem to drive anywhere they like, officially they're meant to be on the left.
Motorcycles get everywhere. The locals refer to them as a swarm of flies. If you don't know what side mirrors are for, you soon will.
People flashing their headlights means 'don't go' - the opposite of what it (normally) means in the UK1.
When overtaking someone, it's a good idea to sound your horn repeatedly so that the vehicle you are passing knows not to pull out. This may at first seem to be quite an aggressive way of driving, but it's for your own safety. Even if you are overtaking someone, it's not unknown for the car behind you to overtake while you're overtaking.
Also be aware that although drinking and driving is illegal in Thailand, some people still do it. You may be sober, but other drivers may not be.
If there's an accident it's your fault. No, really.
You will get stopped by the police for doing what everybody else is doing. Pay up and live with it.
First (and second and third) impressions of the roads in Thailand will have you thinking that driving is impossible. It works because everybody on the road knows what to expect, but don't forget that you don't know what to expect.
Before going to Thailand to drive, practice what you learnt in your driving lessons, particularly how to use your mirrors and be very aware of what is going on around you. A clear country road isn't an excuse to drive quickly - a motorcycle is quite likely to appear from behind a bush and pull out without looking and you really don't want to drive into them at even 30mph. You can kill an entire family like that.
Getting a Car
Cars can be hired at airports and there are many small private hire companies scattered all over the country. A car should come with insurance, but check this before driving off. Get an International Driving Permit2 as you will need this. A reasonable saloon (auto or manual) should be about £20 per day.
Getting Stopped by the Police
The Thai police are... well, they're the police. If you're stopped by the police you will get a fine. Fines are about B400 (about £6), but you may be asked for less; around B200 (about £3) is a common amount.
Whatever you do, sort things out at the side of the road. Don't argue. You did something wrong (even if you can't understand what it was) and give them the money they ask for (but be discreet when handing it over - folding it in your licence or handing it over under your licence is normally best). Don't argue. It'll cost you more if you do and cause more inconvenience to everybody.
You won't be able to tell if the police officer is genuinely giving you a fine or pocketing the money as a bribe. Although there are some officers who do earn money from bribes in this manner, not every policeman is doing this. Even those that do pocket the money3 are trying to make the roads safer and will only target you if you did something wrong.
Having an Accident
If you have an accident then don't move your vehicle at all. The police will turn up and you should try to get your insurance company to come as well. If you're renting a car then ask them what to do and who to contact before you drive off.
It's normal to park without putting on your handbrake (but only where the car won't roll away). It is also normal to double or triple park and to park so as to block others in at a car park. Always try pushing cars out of the way if you're blocked in.
Never put on your handbrake if you're blocking somebody else in. You will not be popular.
Although parking appears to be a free-for-all, the Police do write out tickets, so you cannot just park anywhere. Most of the no-parking signs will be written in Thai, so they won't be of much use to you, unless you can read Thai of course.
Don't park by a kerb that is painted red and white, or in front of railings that are painted red and white.
Getting Away with It
Even getting stopped and fined by the police isn't the end of the world. So long as you haven't hurt anybody, driving in Thailand is a very good way to get a good look around.
Once you learn the ways of the road in Thailand, it is a great place to drive (or motorcycle) and a superb way to see a lot of the country that many tourists miss.
1 This is actually what it's meant to mean in the UK too, but it isn't often used correctly.
2 Available at many main UK post offices for £4 or from the AA. Bring a passport photo.
3 The Thai police officers that you see on traffic duty will normally be earning B6000 to B7000 per month (about £100).
Source: h2g2 (Thanks - couldn't say it better)