How to fix my focus?

Okay so I just got a new camera, a Nikon D3100. When I press the shutter-release button half way down it won't focus. Does anyone have any clue how to fix this?

Have you read the Instruction Manual, for a start?
My guess is that you have it set to Manual Focus instead of Auto. You will have to change to Auto focus but I don't know the method for that with Nikons

All of your answers are in the manual.

What focus mode are you in?

See page 16 in your manual. Be sure the switch is in the A or M/A position.

Two possibilities:
1. The lens is set to M instead of AF or maybe that's on the body.
2. You have turned the AF off at the shutter button and on at the rear AF button. If you haven't done this, then you should. Using the rear AF button allows you to focus once on your subject and then take all the shots you want with various compositions without the camera re-focusing. Refocusing also takes up time, granted a small amount of time with the D3200, but nonetheless, with the AF system set to the rear AF button, you will practically zero lag time between pressing the shutter button and the camera actually taking the shot. Also, if your subject is off center you can use the center point AF, focus on the eyes and then regardless of where your subject is within the frame, you can take shots without having to worry that the camera is going to re-focus on the background or something else that you don't want in focus.