First look at what your computer can support. What kind of slot do you have? If you have a Radeon 9000 series, then it'd be AGP, which will certainly narrow your options down. Second, your power supply can potentially be a limiting factor. Many cards now require an additional power connection, and will consume a fair amount of power. Many consumer desktops from companies like Dell or HP come with very modest power supplies that may not be capable of supporting a power-hungry card. Space may also be a concern, since the further up the product lines you go, often, the cards get physically bigger (to a point) and harder to fit into a case.
Second, to a point, decide what level of performance you need and/or a budget to work with. IE, if you only play a few older games, then you don't exactly need a $700 card, but you'll probably benefit from something in the $100+ range at least.
The size of your monitor can also play into this, since it takes considerably more horsepower to max out settings at 1920x1200 than it does at 1024x768 (as an example).
Model numbers don't tend to tell you that much if you are unfamiliar with the product line. I mean, within a given lineup, usually, the higher the number the better. Often you will have a larger number that denotes the entire series, IE, Radeon HD5000. Then the overall tier, such as HD5400, HD5700, HD5800, etc. Inside those, you'd find individual models, such as the HD5450, HD5750 and HD5770, HD5850 and HD5870. Logically, a 5850 is better than a 5770, which is better than a 5450 (by quite a lot), and so on. However, you're better off doing some research to get a general idea of the type of performance that the models give.
In terms of specs, there are usually two big ones that will vary. The actual GPU, which is typically denoted by the model number, and the amount of memory the card has. Most of the time a given GPU will have maybe a couple memory configurations, IE, 512MB or 1GB.
Secondary to that would be how fast those items are clocked, and for some cards (usually more on the low end), the type of memory used (and possibly in turn the memory bus width).
90% of the time, the clock speeds will be pretty much the same for the same model card from different companies. The rest of the time, you may have models that run slightly over, or slightly under the reference design.
If you are looking at a low end card, for one reason or another, and there are variations on the memory, for example, models with DDR2 memory and DDR3, then the higher ranked memory cards will often be notably better, albeit a little more expensive.
Most of the time though, you'll combine what you can put in your computer + budget, and narrow things down to a handful of cards. The individual features/specs of a particular model line might come into play at that point, but for gaming, usually it's just a matter of finding what card performs the best unless you have a very specific want/need for another factor.
Here is a buyer's guide that has some picks per price point. At the very least, the hierarchy chart at the end can give you a general idea of where a given card stands.