Getwork
An RPC method used by a miner to get hashing work to try to solve.
Pseudocode
(Just ignore the midstate until you understand the internals of SHA256.)
calculate: hash = SHA256(SHA256(data))
If that meets the difficulty, you win!
If not, increment the portion of the data that starts 640 bits in (bytes 76 to 79), and try again.
If the incremented portion overflows, get new work.