your graphics card makes attempt at a random code
it's like guessing a random set of numbers, say 1-10
you card will guess in order until it guesses the correct number, then you get a share
a certain amount of shares are in a block, usually in the tens-hundreds of thousands, sometimes millions
when in a mining pool, everyone works together to get all the shares in a block and everyone gets paid according to how many shares he found
if you mine solo, you have to find all the blocks and then you get all the 50 BTC in the block
you can mine with your CPU, but it's really slow
if you have a radeon 5830 you can mine with 250-300 Mhash/s, with a pentium duo core you can mine with 2 mhash/s