When buying lenses for Nikon D5100?

Please forgive my ignorance, but I don't know anybody who is into photography. When buying a new lens, how do know if it is going to fit my camera. Do all Fmount lenses fit and how will I know if the lens has a built in motor?

Sorry for asking such a dumb question.
Thanks!

Added (1). Thanks for the info, but you forgot to tell me if any Fmount will work.

There should be a list in your manual (and on Nikon's web site) of which F-mount lenses will work on your camera, not all of them will. Anything without a focus motor is manual focus only, of course, and there are some that just can't mount at all.

Very common question.

For a D5100 you want motorized lenses. Nikon calls those AF-S. Sigma calls it HSM and tamron calls it build-in-motor. Tokina doesn't have a real name for it yet, they refer to it as "built-in AF motor drive. "

With the non-nikon lenses do be sure it says for nikon or nikon mount on the box.

EDIT: OK…

Pre-Ai F-mount lenses are not officially supported, they should mount but may cause damage.Ai and Ai-s manual focus lenses will mount but work in M mode only.AF lenses will mount and work except you will need to focus yourself.

It's not a dumb question, Nikon lens compatibility is a science in itself. The digital compatibility table in Ken Rockwell's Nikon Lens Compatibility list should tell you what you need to know (see link below).

In theory, virtually all of Nikon's F-mount lenses made since 1959 should fit your D5100, with the exception of a few exotic fish-eye lenses which have rear lens elements that stick out and could damage the camera's mirror.

However, there's more to it than just bayonet mount compatibility; modern lenses have a number of electrical contacts that relay distance and focal length information to the camera body, necessary to calculate exposure, flash intensity, auto-focusing etc.

That's why you should look for AF-S or G-lenses if you want to be able to use all the functions of your D5100 (or their non-Nikon equivalents of course). Older Nikon lenses such as the AF-D series will fit but primary functions such as exposure metering and autofocus won't work.