There are numerous programs to overclock with. Coolbits, Rivatuner, ATI Tools (can use with nVIDIA card too) are a few out there on the Internet.
To simplify, never overclock more than 5-10MHz at a time. Say you have 400/1100. Overclock to 410/1110 and benchmark to test. Two ways to test stability and make sure there's no tears or screen doing funny things: 1) Play a game of your choosing (preferably high-stressing games like Quake 4 or something). 2) Benchmark softwares like 3DMark01SE, 3DMark03, 3DMark05, 3DMark06 are really good at stressing your video card to the max.
Rinse and repeat. When you're satisfied with your final core/memory, run 3DMark (05 or 06) a couple of times; if the computer didn't freeze and go crazy, you're pretty much set.