There are many different ways to drift a car - below are different techniques on how to do this,
(Note: ABS and TCS should be turned off before attempting to drift. These systems are not made to take into account a driver wanting the car to slide. Also, please do not practice this on the road, but at a MRT Track or Skid Pan Day or other safe venue that is not a pulblic road).
Braking drift - This drift is performed by trail braking into a corner so that the car can "set" or shift weight to cause the rear wheels to lose traction, then controlling the drift with proper steering and gas inputs. Having brake bias can be beneficial to the drift depending on the driving style. Usually having bias on rear brakes helps to brake drift.
Power Over Drift - This drift performed when entering a corner at full throttle to produce heavy oversteer through the turn. It is the most typical drifting technique for AWD cars (predominantly RWD). Keiichi Tsuchiya has been regarded as saying he used this technique when he was too scared to drift at certain corners when he was younger. However the chance of this technique leading to a burn-out instead of a drift is possible if executed at a bad angle.
Inertia (Feint) Drift - This is done by rocking the car towards the outside of a turn and then using the inertia of the car to swing it back to the desired drifting line. By going away from the corner, and turning back in hard, you are coming from a much sharper angle. Somtimes the brake will be applied while rocking the car towards the outside to give a better weight transfer; hence creating an even sharper turn. It has been said by many pro-drifters that this is one of the hardest techniques to master as has a high spin-out factor.
"Lift Off" - At very high speeds, by letting your foot off of the accelerator while cornering, certain cars with very neutral handling, such as the MX-5 or 200SX S14, will begin to slide, simply from the drop in torque and engine braking. The drift is controlled afterwards by steering inputs from the driver and light pedal work.
Handbrake/ebrake Drift - This technique is pretty straightforward; pull the handbrake to induce rear traction loss and balance drift through steering and throttle play. Some people debate the fact that if using the handbrake creates an actual drift, or just a power slide, but ultimately, using the e-brake is no different than any other technique for starting drifts. This is generally the main technique to perform a controlled drift in a FWD vehicle. This is one the first techniques beginners will use as their cars are not powerful enough to lose traction using other techniques. Also this technique is used heavily in drift competitions to drift big corners.
Dirt Drop Drift - This is done by dropping the rear tires off the road into the dirt to maintain or gain drift angle without losing power or speed and to set up for the next turn. Only permissible on roads without barriers and lined with dirt or other materials which to lose traction. This is commonly done in WRC rallying.
Clutch Kick - This is done by "kicking" the clutch (pushing in, then out, usually more than one time in a drift for adjustment in a very fast manner) to send a shock through the power train, upsetting the car's balance. It causes the rear wheels to slip and enables the driver to induce over steer.
Choku Dori - This is used while drifting on straightaways. The driver of the car sways the car side to side while the car is in a drift, which looks impressive. It can be initiated through all the above techniques.
Changing Side Swing - This technique is used extensively in the Japanese D1 competition and is very similar to inertia (Feint) drift. It is often done on the first entry drift corner, which is often a long double apex turn just before a very fast straight-way. If the straight-way before that double apex is of a downhill orientation, the driver keeps driving on side of the track that is closest to the corner. Then with correct timing in mind, the driver abruptly changes the car onto the other side. This movement has the car momentum to be altered causing the rear wheels to lose traction. The car is in a drift motion right now. Then the drift is carried over into the corner and through it.
Dynamic Drift - This technique is similar to the Choku Dori. It employs all forms of the above techniques - and not restricted to only one - in combinations to accomplish the desired drift movement.