Discrete or Integrated?
Okay, it's time to make a buying decision. Do you go with a discrete graphics card (in either a desktop or notebook) or integrated graphics? If you want to play games, even just a bit, you'll have a far better experience with discrete graphics.
If all you want to do is browse the web and do some light word processing or email, integrated is probably enough. Intel's integrated graphics isn't as good as Nvidia's or ATI's, and if you care about the quality of the video (watching DVDs or downloaded video on your PC), you want an Nvidia or ATI graphics chip. If battery life is your top concern, avoid discrete graphics and go with integrated.
How much should I spend?
As a rule of thumb, you should probably not spend less than $100 or so on a graphics card. Cards in the $99-149 range offer a lot of bang for the buck and can run almost all modern games very well. Once you start spending less than that, the performance drops rapidly and you'll just need to upgrade sooner.
If you or someone who uses the computer is a more serious gamer, look for cards in the $179-229 price range. These offer great performance without breaking the bank. You really don't need to spend more than that if you're reading this article. Those high-end graphics cards are for the sort of graphics and game fans that don't need a "Geek 101" type article.
How much memory do I need?
You'll see a lot of cheap graphics cards with 1GB of memory on them. This is mostly a waste of money. In the $100 range, there isn't much benefit to having more than 512MB of memory. A faster GPU chip on the card is worth more than a bigger amount of memory. Once you get to the $149-and-up range, you want a card with 1GB of RAM. If it's integrated graphics, it'll use your main system memory and you don't need to worry about it (this memory sharing is one of the reasons integrated graphics are so slow).