Basically, distributive computing is done by breaking up whatever computer process you want to perform into pieces that individual computers can execute. This pieces are processed by any computer in contact with the internet and can be run in the background. In reality, our processors aren't used very much when we're not looking at the screen doing stuff, so might as well not let our little Intel's or AMD's go to waste, right?!
The program that SETI uses (and a few other groups too) is called BOINC.
Boinc sends you different jobs to run and once completed they get sent back and you are given credits. These credits are added up to show how much work you have done. You can also join other groups to have your credits help them out (BYU has some groups...hint, hint).It's a really cool system and you can use the GUI output of the program as a nifty screen saver. I am currently running two different processes: one for SETI and the other is called Rosetta. (though I can't get my screensaver to work now, though maybe that's a Vista problem...) Rosetta is a program that runs protein folding simulations using energy minimization principles. (there's even a protein folding program that uses your graphics card to run programs, called folding@home, which is not affiliated with Boinc)
It's a really neat idea and I can feel so warm and fuzzy by letting other people use my computer to help in the cause of science! (Yeah for me!!)
Here's some screeshots from the web of SETI@home and Rosetta:
