Is this lens compatible with my Nikon D5100?

I'm looking at purchasing the Nikon ED AF Nikkor 70 - 300 1:4 - 5:6 D Lens used from a local photographer, but before I do would like to confirm that it is compatible with the Nikon D5100?

I know the 5100 needs the lens to have a motor in it or something for autofocus… Is that correct and does this lens have it?

I have experience with DSLRs and photography but am clueless when it comes to doing things other than actually USING the product!

Nikon made 3 different 70-300mm lenses.
The 70-300mm AF-G was a very plastic lens that had good performance, but wasn't well constructed. I know this as my copy "snapped" after being bumped during a shoot.
The 70-300mm ED AF-D lens is better made, and has slightly better performance.

But, the 70-300mm AF-S VR lens is the only version that has the internal auto-focus motor that your D5100 needs.

The 70-300mm AF-S VR has excellent reviews, but does cost quite a bit more than the other two models. For a more economical choice, you might look at the Nikon 55-300mm AF-S VR.

I wouldn't buy it unless you can get it for really, really cheap. With no autofocus (AF-S lenses autofocus on your camera, AF ones do not) and no image stabilization (VR) you won't get much fun out of this lens. You'll struggle to obtain sufficient shutter speeds for a steady shot without a tripod in anything but bright sunlight (that's why VR is important), and focusing will be a nuisance.