I saw a list of supported cards a while back, and it looked pretty friendly. You might have trouble on a laptop or something, but if you've purchased a gaming computer in the last five years or so, then you should be able to play. SWC
Have you been able to play games released in the last three years? If so, then you should be able to play Diablo 3. SWC
I don't know if this will show up for everyone or not, but according to this the minimum requirements for a PC are NVIDIA GeForce 7800 GT or ATI Radeon X1950 Pro with the recommended requirements being NVIDIA GeForce 260 or ATI Radeon HD 4870. Diablo III System Requirements - Battle.net Support