This is a very old thread and lots of good information is already posted. However, this technique hasn't been mentioned. This is also for non
-racing transmissions (like a Muncie, T-10, etc.) that are not
designed for clutchless shifting. If it is a spark ignited vehicle, wire a normally-off push button to the ignition. The idea is to be able to kill the motor by temporarily pushing the button. With engine under load and accelerating, you rest your hand, or apply a slight shifting pressure, on the shift lever. You then briefly hit the kill switch and the trans will pop into the next gear. This is an incredibly fast shift and brutally hard on the entire drive train! As already mentioned, eventually you will break parts! But it does work and is fast enough to win a race. YMMV
EDIT: My apologies to birdman above. His technique is fundamentally what I am talking about which is a method to temporarily interupt the powerflow. With tweaking his method could be more precise. My method is quick, cheap, and with more timing variability due to your response time.