We've already mentioned how to overclock your card with RivaTuner, but if you're a bit more of a casual gamer looking for a bit of mild tweaking, you may find Precision is more your speed. Most of the settings are available in Precision's small window: you can tweak the core clock, shader clock, memory clock, and fan speed, as well as link multiple GPUs together. Then, you can monitor your card's temperature, clock, framerate, and lots of other things either from Precision's screen overlay (so you can see it while gaming) or its smaller, less intrusive window (which is great if you have dual monitors).
It doesn't have as many features as RivaTuner, but it's also very simple to use: just adjust the clocks and hit the Apply button. I'd still recommend doing a bit of research on how to test your overclocks for stability (this guide is fairly helpful), but it shouldn't be too much trouble.
If you're not looking for an incredible overclock, you can always just set it near the levels of the "superclocked" version of your graphics card—which is essentially a pre-overclocked version of a video card available from the manufacturer. It's a good benchmark of what your card can easily handle, and you don't have to spend the money on the pre-overclocked card to get the performance boost. Hit the link to check it out, and if you've used a tool like Precision before, share your tips in the comments.