Instructions
Pick the "Manual" setting instead of "Automatic" after you have selected your player. The power slide can only be done when players use the "Manual" setting.
Round corners holding down the "Drift" button, which is "B" on the controller. Continue to hold the button down as you slide. You will still be able to control the direction of your kart.
Watch for blue sparks to shoot from your tires as you slide. Once you see these, release the "Drift" or "B" button to get a power boost and do the power slide. Both karts and bikes can do the power slide in Mario Kart Wii. Karts do get a bigger boost than bikes.
Wait for and even bigger boost if you have a kart. The blue sparks will change to yellow sparks if you have a kart instead of a bike. Releasing "B" when you see the yellow sparks will give you an even bigger boost than with blue sparks.