What kind of car do you need?
Rear wheel drive is essential to perform sustained doughnuts, and you'll need enough power to spin the rear wheels and keep them spinning. This is a technique you won't want to use too frequently unless you have a set of rear tyres which you don't mind wearing out! Make sure all stability control systems are turned off, and it you are in an auto, lock the gear in first if possible.
Do not attempt this technique on the public roads!
How to do a doughnut
You can perform a doughnut in two slightly different ways and you don't need to be too hard on the clutch to pull one off. You can either have a rolling start, or spin the wheels from a standstill...
1. Spin the wheels. It's slightly kinder to your car to have a rolling start, this will allow you to fully release the clutch before inducing wheel spin. Approach the area where you want to perform the doughnut in first gear at low speed, ensure you're completely off the clutch then turn in hard and apply full throttle rapidly.
2. If you have enough power you'll find the rear wheels start to spin. Keep the revs up high in the power band and apply a certain amount of steering lock . Alternatively you can spin the wheels from a standstill while applying some steering angle to have the same effect.
3. You should find that the rear wheels lose traction and begin to cause the car to rotate, keep the revs high (you can even remain on the limiter if fitted) and you should complete a doughnut. You can modify the direction by steering at different angles and altering the throttle.
4. If you want to drive away from a doughnut ensure you make the necessary counter-steering adjustments early as the car will have a tendency to oversteer.
In summary a doughnut is a relatively simple and dramatic technique to perform with the right car.