On the P3's, Tbird's, Duron's, etc. you only put a small amount on the core in the center of the chip. You want a relatively thin layer, a small gob and then spread it. Some people say to smear it evenly over the surface of the core with wooden popsicle stick. Then you put the heatsink on carefully, and wiggle it a little bit to work out any airbubbles. All you want it to do is fill in all the little spaces between the CPU and Heatsink. Too much is actually a bad thing.
To get an idea of how much you actually need, take a look at a heatsink that has the crappy thermal tape on it, that has been running in a system for a couple days. The actual layer that remains where the core sits is less than paper thin, with all the stuff around it intact. It's like a little square burned into the tape.