Dont do the manual thing that christer said, its just easier and better to let ATI Tool to do it all for you. Btw Christer running artifact scan for 2 mins wont help much coz it may run for 2 mins with no artifacts but not for 10 mins because of the heat that it will produce after running at a higher speed + longer time.
1) Find Max Core ~ 30-60 Minutes. Keep a watch on ATI tool because it will restart and start all over finding max core when it hits the point it cannot go further. (so after 1 hour go and stop it and look @ the logfile to see what the highest OC was).
2) Do exactly the same as Step 1 except using "Find Max Mem".
3) Now u have your results of the highest core oc/mem oc you can have, Subtract 15Mhz off the core and the mem results u just got. Set your clock speed at those values and then run "Scan for Artifacts" for as long as you want (I'd suggest +-2Hrs).
4) If it finds artifacts, then either get better cooling for your gfx card OR take some more mhz off each slider. (obviously then run scan for artifacts again until ATI Tool cant find any artifacts).
Remember, you should get proper cooling equipment for your gfx card when OCing it!