You can OC using the CCC (Catalyst Control Center) - which is the AMD default utility, although the OC in the CCC is generally limited by the card bios.
For example my 6850 can only go to 875MHz core on the CCC, don't remember the memory limit. You just click the key symbol to unlock overclocking, move the slide bar to what level you want ant press apply. Mine is running at 875/1200.
If you want to go higher you use an utility called MSI Afterburner, that let you surpass the CCC limits. 900-950 core on 6850 without voltage shouldn't be hard to achieve at stock voltage. Adding voltage might allow you to go higher.
It can increase the speed of games somewhat, depends on the game and such and such. A 6850 @950/1100 should be quite close to a 6870 performance.
The downside is increased heat and power consumption. I would be careful OCing with that OEM PSU that came with your PC.
This a
review of 6850 OC'ing and its impact in some games. It also talks about using MSI afterburner.