The best
tip I can give you to get better is to play, and play often, but if you
are a true Kart lover, this is no problem.
I believe
that the best way to turn corners is with a rapid tapping of the "B" Button.
It slows your speed just enough to make it around without wiping out, but
doesn't diminish you speed completely (Like letting go of the "B" Button
would).
When you
acquire a banana peel or a green turtle shell (That you don't intend to
shoot), drop them in the middle of a straightaway. The computer players
follow an almost exact path around each of the courses, usually heading
for the center of the road on straightaways. Learn their paths and you
can spin `em almost every time you drop something.
If you are
playing a two player game, and the other player acquires a RED turtle shell,
here are some ways to dodge it.