Nikon D3100 able to shoot the night sky?

I would like to take pictures at night of the sky and get some galaxy kind of type pictures is this possible with my Nikon and if so what type of lens would work and how do I do it?

Yes, it's capable you'll need a tripod, though - look up, 'Astrophotography.'

Whole libraries have been written on the subject, though.

Yes, you can shoot the night sky.

Taking pictures of galaxies requires a tracking telescope because the earth moves during the long exposure time. If you just want a picture of the sky, and a fairly wide angle view, then you'll need a lens with a wide maximum aperture to get the shutter speed below around 30 seconds. Beyond that the stars won't appear as individual dots, but as streaks.

You'll also need a tripod and a cable release.

If you set the camera to long exposure NR, you should be able to get okay shots of the night sky

There's a problem shooting the night sky with ANY dSLR.

* long exposures will create star "streaks, since during the time the shutter is open, the earth is moving.
* unless you are far away from "city lights" only the brightest stars will show through the light pollution.

My guess is you want to get photos like those found on the NASA websites. Those photos are shot with a totally different camera/lens system

If you are still interested in shooting the night sky, look into buying a telescope which has a motor that matches the rotation of the earth so that the stars or planets you shoot come out sharp.

The cost of the adapter you will need is less than $50

Set your white balance to the daylight pre-set.
Getting a good infinity focus with the kit lens can be tricky. You want a tripod with a quick release plate. Zoom to 18mm and try to lock autofocus on a distant street light or similar target. You might be able to illuminate something with the car's headlights. Then switch from autofocus to manual, being careful not to disturb the setting. Do not change focal length, because the lens may not have the same focus point.
As for galaxies, don't expect much with simple equipment. 18mm, f3.5, 15 seconds, ISO 400, I think maybe the core of the Andromeda Galaxy M31 might be visible, but just the brightest part of the core, so it may not look like more than a faint star. Capturing the spiral arms would take a much, much longer exposure, which would require an equatorial drive to avoid noticeable star trailing.
You might be able to capture a hint of the nebulosity M42 in Orion's sword.
You may or may not gain a little bumping the ISO up too 800, but beyond that mottling from noise will certainly be greater than any possible nebulosity you could capture.