Diddy Kong Racing is just all kinds of weird. You have anthropomorphic animals racing go-karts around an island to get magic balloons from a blue elephant-genie to liberate said island from a maniacal wizard pig. Standard stuff.
One of your choices to help liberate the island is a diminutive mouse named Pipsy. Pipsy is a little slow, and kind of light, so she's hard to control. But if you can control her, oh man, you've got something here.
One thing you have to know is the controls. Your basic controls are A to go forward, B to brake, and R to do a sliding turny-thing.
Two things to remember, then, is: the slower you go, the tighter you can turn; and pressing R to turn means you can take a slide around a curve and turn without losing much speed.
The thing we want to do is combine them into one super-technique. Let's take a course, any course at all. How about... Star City?
The thing about Star City is that it has these brutal right-angle turns right in the middle of the track. Lame!
But if you combine the gas, the brakes, and the slide-turn-thing, you can totally take the turns without even touching the walls. She hugs that track like it's velcro.
Which is kind of tough to see in these shots, so I've prepared a (4MB) animated .gif file to show it in action here. I almost botch it because her control is just so tight. Pretty awesome, really.