Are you looking for a point and click or a more complex machine? What's your budget? How savvy are you with the computer, do you need software to download it all for you, or can you do it by hand?
The most important thing IMO is to get a camera from a big name (Canon, Nikon, Olympus, etc.), there are literally hundreds of little guy cameras, and while some of them may be decent, most of them are not, IME. I always go for Canon... my mom was a Canon fan, and i just sort of inherited that.
If you're anywhere near a decent sized city, I'd definitely look for a camera shop. You don't have to buy the camera there (they're usually more expensive), but they usually have very knowledgable people working there that can answer all your questions, as well as letting you hold and play with the camera you're considering.