For a nikon d5100 camera will an old lens like a 135mm f/2.8 Nikkor-Q Auto work?

I'm a very beginner photographer and i was just wondering if I could purchase older lenses to start off with and would they fit?

Nikon lenses made since 1957 (F-mount lenses) will physically mount on the camera. But that's just a third of the things that a lens should do.

The very old ones won't give you light meter readings nor autofocus, and old ones won't autofocus on your camera. I'd skip any lens that does not say AF-S in its description (merely AF is not enough, you need AF-S!) Otherwise it won't autofocus.

Here is a table which says what kind of lens will work with what kind of Nikon camera:
http://www.kenrockwell.com/...y-lens.htm

The lens that you mentioned would fall under the pre-Ai category in this list.