Try out any games you have, watch a DVD, view some screen savers maxed-out, observe some text in a document, etc. Keep in mind that some games might act screwy if some video options are enabled in which the game wasn't meant for such as anti-aliasing, or triple buffering.
Alternatively, you can download one of the many benchmark utilities such as 3dmark and run through a few benchmarks. These benchmarks will run the gamut of video settings and test OpenGL, DirectX, rendering, blah, blah... But, keep in mind that these benchmark programs are meant to bring even the top-dog graphic cards to their knees so don't fret if you see lagging on 1600 x 1200 res, 8x anti-aliasing, super quality settings. Of course you shouldn't see any lagging in everyday apps or medium settings.
What you should pay more attention to are visual artifacts that appear, lines or streaking, unwanted pixelation, missed color representation, etc.
RP