I'm sort of assuming you're building a PC to some extent, rather than just buying one off a shelf?
Graphics cards have a lot of different numbers to compare. Not nearly simple as ram or CPU etc.
If you know you want multiple monitors, or your monitors have particular connectors your graphics card needs to have, that is a superficial way to narrow down your search.
Generally, better graphics cards have more memory. It is fairly safe to assume that a 2GB graphics card is better than a 1GB card, though it is a lot deeper in reality. That gives you a start when you're looking at a card.
When I am getting a new graphics card, I like to look at the steam hardware survey.
http://store.steampowered.com/hwsurveyIt shows what's popular with gamers right now. I go down the list until I find one that's in my price range and read some reviews to check no big problems.
This site has benchmark statistics on different graphics cards. If there are a few you are looking at, or you want to see if it's really worth shelling out for the next model up, this comes in handy.
One thing to look out for is power requirements. Modern graphics cards normally need more power than a pci-e slot can deliver and will have an additional power connector that you plug into your PC power supply. Before you buy a graphics card, check the connector on the graphics card is a connector your PSU has. There are different size connectors (8 pin, 6 pin etc) and there's no guarantee your PSU has the right one. I expect there are probably adaptors mind.
It's worth just checking your power requirements don't exceed the maximum power output of your PSU also.
If you're buying a tower off a shelf, some/most of the above may not apply...
