In Mario Kart 7 for the Nintendo 3DS, you can drift around corners to gain a slight boost.
To drift, you simply press and hold the Hop button (the R button) while going around a corner. Your tires will light up blue at first to show that you are drifting, and when you have drifted enough your tires will light up red and you can let go of the drift and get your boost.
Drifting will take some time to master. Remember that you can keep steering left and right during a drift to modify your drifting angle, which is one of the big keys to drifting effectively.
Timing the start of your drift is also very important. Typically you’ll need to start drifting a little early, and some karts drift better than others, so it’s something you’ll have to play around with a lot in different karts.