What's the difference between dedicated and shared memory, and how much of each is a good amount?
In the case of dedicated memory, the video memory is on the card. The video card itself holds that amount of memory. With shared memory, it "borrows" from your system memory. It's pretty much useless, because it's bound to be very slow compared to real video memory.
A good amount depends on what you plan to do with it. 256MB is the general amount, so aim for that.
But remember, that's really not an important part of a video card. There are other things that matter much more than memory. You could have a crap card with 512MB memory, while something with 128MB could be much better.
If you tell me what you're looking for, I could help you out a bit. It's something you basically need to learn from experience, because there's not a single thing you can look at to tell how a card would perform. You just need to know the models.
If you're looking into cards that have shared memory, you're probably looking into terrible models. It's usually lower end cards that have shared memory, generally called TurboCache for nVidia cards. It's best to avoid those if you're aiming to play games.