If you're serious about getting good, find a manual camera. The "point and shoot" cameras with autofocus and autoexposure will usually give pretty good results immediately, but great pictures require you exercise your own judgement.
A great camera for this purpose is the Pentax K100. Built like a rock, good feel, and easy to use. And there are lot of inexpensive used ones out there; they used to be the standard camera for photography classes.
But you will have to learn how to focus, and adjust the shutter and aperature.
In a used bookstore, you might find "The Joy of Photography". It's a great and well-presented work on basic photography.
Is there anyone here interested in the working with older equipment like Contax, Leica, Topcon RE, etc?