How to fix my d3100 nikon 1080hd when its showing black when i'm tryna take photos?

Soon as i try to record a video or take a photo the screen go black and when i look through the sight it black as well.

You question is not very clear

When you use your camera as a still camera (its main function) and look through the viewfinder, what to you see?

Except when shooting video, you need to learn to use the viewfinder as seen on page 25 of your user manual. This assures that you create the most stable platform for shooting your still images. Holding your camera at arm's length like it is some huge P&S camera can only cause burred image at shutter speeds the should produce sharp images without any blur if you use the cameras viewfinder.

When it comes to shooting video, you MUST assure that there's enough light. Just because you think there should be enough light, does not mean that there really is.

Here is what can be happening. In the video mode, the shutter speed is fixed. That means that the only way to control exposure is by allowing the camera to open the lenses aperture (possibly creating a shallower depth of field than wanted) or automatically increase the ISO setting, which will increase noise. The other way to assure a proper exposure during the shooting of video is to add more light, add it in a way that emulates the existing lighting, just like they do in Hollywood

Set the camera to P mode, Auto ISO, Auto white balance, AF on and EV to 0, then go out. Look for a brightly colored car parked under the sun. Take its picture from about 12 feet. If nothing comes out, press the Preview button (triangle). If still nothing comes out, try the video at Auto everything too. If still nothing comes out, you will need to have the camera serviced. The digital sensor may already be dead. It will cost you.