Instructions
Select "Practice Mode" from the main menu and pick a track with wide, sweeping curves, such as the Greek track or Circuit de la Sarthe. If the curves are too sharp, drifting becomes nearly impossible to pull off.
Select a car with decent horsepower (more than 300) and an automatic transmission. You can perform a drift with manual transmission, but switching to automatic allows you to focus on your steering and acceleration.
Accelerate toward the curve with the "X" button at approximately 70 or 80 mph. Your car must be on the threshold of control loss when you enter the curve, so adjust your speed according to the handling characteristics of your selected car.
Release the "X" button and quickly oversteer toward the inside edge of the curve with the directional pad.
Correct your steering once your car begins to slide by quickly steering toward the outside edge of the curve. With enough momentum and the proper timing, your car will drift through the curve without issue.
Press the "X" button to give the car some gas when exiting the curve. If the curve is of the larger variety, you will need to tap the accelerator over the course of the drift to keep the car from spinning out.
Practice your drifting on the same curve from the same direction until you master that particular section of track. Try different curves from different directions to develop your drifting skills.