I'm using a D3100 D nikon?

I'm using a D3100 D nikon. I just wanna know is AF-S VR Nikkor 70-300mm f4.5-5.6G IF ED compatible with my camera.

Yes. The AF-S VR version of the 70-300mm will autofocus with the D3100.
Long focal lengths magnify camera shake. The VR can help, but you would get best results with a tripod. Get a good tripod, not a cheap one. Besides the possibility of magnifying every little vibration at 300mm, this lens is making your camera front heavy, and a flimsy tripod can sag under its weight. Even a good tripod may droop a little bit just as you lock it into place. When using a tripod, you should turn off VR.

Yes. Any Nikon lens for DSLRs will fit on any Nikon DSLR made since 1959, when the F-mount was introduced.

Since it's an AF-S lens, it's also gonna autofocus on your camera, so you're good to go. An AF-D lens wouldn't autofocus, so be careful when buying those.

But yeah, the lens you want will work perfectly fine with your camera.

Yes it is.