I wrote a driving guide a long time ago.  I'm gonna cut and paste the section on drifting, lets see if this works...
5. Advanced Techniques
5.a. What is the difference between drifting and sliding?
Drifting is a sort of controlled loss of control of your car.  When you drift, 
you use the weight and momentum of your car to move it laterally while it is 
still moving forward.  In most cases, drifting is meant to bring the back end of 
the car around a turn faster than the front, while countersteering with the 
front wheels to maintain control and proper vehicle attitude.  Alternately, a 
drift will occur when exiting a turn, when your outside tires are overloaded and 
lose traction, forcing your car toward the edge of the road.  This is desirable 
because you can reach greater turn exit speeds by travelling at or near full 
throttle, but only if you can regain traction before your car slides off the 
road.  Drifting is a knife-edge sort of driving technique, where you must be 
smooth and remain in control or else you will either slow the car unnecessarily 
or spin out.
As opposed to drifting, which is a controlled technique, sliding is a more wild 
technique with less control.  A slide (or powerslide) occurs when all four 
wheels break traction and simply scrub along the road, accompanied by frenzied 
screeching sounds.  Sliding is, in nearly all cases, slower than drifting for 
several reasons: First, you have no or very little traction during a slide, 
eliminating control of your car.  When you are sliding, you cannot properly 
position your car for or during a turn as quickly and easily as you could while 
drifting.  You must first slow your car until you regain traction, then adjust 
attitude.  Secondly, you cannot accelerate as fast from a slide as you can from 
a drift.  In rear-drive cars, properly accelerating from a drift will cause the 
rear tires to regain traction, providing acceleration.  With a slide, you must 
again slow enough to regain traction before giving the car gas will do any good.  
The only time sliding is a useful technique is as a last-ditch effort to avoid 
going off the road or colliding with another object.
In any case, it's best to read the reference manual that came with the game, as 
it goes in-depth on the technique of drifting, and practice your techniques in 
Time Trial mode.
5.b. How do I drift?
A more complicated way to drift is by using the gearbox.  By downshifting as you 
enter a turn, you momentarily lock the rear wheels (the same effect as hard 
braking, except without slowing down as much).  This causes them to lose 
traction and drift the rear of the car out.  If done correctly, the front tires 
will maintain traction, allowing you to control the drift.
And a yet harder method is 'trail braking'.  In the game, this is much easier 
and more effective to perform with an analog controller than the digital control 
pad.  When approaching a corner, brake as usual, but instead of totally letting 
of the brake as you turn, gradually reduce pressure on the brakes as you turn 
in.  This shifts weight to the front of the car, but no so much that the front 
tires are overloaded, and the combination of reduced weight and braking effect 
on the rear tires causes them to lose traction.  This technique is superior to 
the others because it can maintain more speed and it is easier to regain 
traction in the rear wheels, but it is also much harder to master.
Again, it's best to practice these techniques in Time Trial or Arcade mode until 
you feel comfortable with them.
5.c. How do I control a drift?
Controlling a drift is very hard to do correctly, because each car is different 
and there's a huge difference in handling with each drivetrain layout.  
Following are some tips for each drivetrain:
FF - With an FF car, simply countersteer (turn the wheels opposite the direction 
of the turn) slightly and reduce acceleration, and your car will regain control.  
To extend the drift, modulate acceleration and steering.  Drifting in an FF car 
tends to lose a large amount of speed, and is only recommended on turn exit, not 
entry or apex
FR & RR - Countersteer aggresively, and modulate the power to the rear wheels to 
avoid spinout.  Lifting off the throttle altogether in an RR will usually spin 
you more than once.  Giving an FR car more throttle will bring the rear end 
slowly and irreversibly around.
MR - In MR cars you'll slide very easily unless you control the drift very 
carefully.  You'll have to correct your car's attitude almost every time you 
take a corner.  Countersteer aggressively, but beware of erratic accelerator 
commands.  This drivetrain requires smoothness and control.
4WD - These cars almost control themselves through a drift unless you set up
your car incorrectly or you're in an insanely powerful car. Watch the car 
carefully and countersteer if the angle of the car to the corner becomes too 
steep.  Some cars have different power splits between the front and rear 
wheels... a car with a 10%/90% f/r split will act like an FR car and be much 
more likely to lose control than one with 30/70 or 50/50 split.