I agree with the don't breaking - use the kart in front for braking purposes this helps to keep your speed up and puts him out as well.
Remember to choke the carb coming out of tight bends (put your hand over the inlet) helps on pick up out of bends (well it works on racing karts - probably won't do much on a rental job though).
At the start, hold the steering wheel and jump up and down in the seat (not joking it works - you should get a better start).
Finally, as above, if possible cheat!