I have the same camera purchased a few months ago. Still learning. First, did you print the manual from the disc that came with the camera? It has way more than the little paper manual you also got with the camera. I printed mine double-sided, and put in a 3-ring binder. I suggest you put your camera on a tripod or on a steady surface so you know you are not moving the camera. As someone suggested before, go outside and pick a subject. Look thru the viewfinder and press the shutter release halfway to focus. While looking thru the viewfinder do you see a round dot in the lower left corner that is flashing? If it is steady focus has been achieved. If the little round dot is flashing that means the camera is unable to focus for one of various reasons. See page 56 of the manual that comes on the disc.
On your lense is the A-M switch set to A or M? If it is on M - then you have to focus manually. Try switching it to A (on your lens) and check whether your camera will focus.
Also, if there are too many places the camera can focus on it gets confused. You can (while looking thru the viewfinder) press the arrow keys up/down left/right to pick one focus point (there are 11 points) and have that point (which will be lit up) that you have chosen on the area you want to focus on.
Also, if you see a ? that is flashing in the lower left of the monitor press the ? button (the buttons to the left of your monitor - should be the 3rd button from the top. Hold that button down and you will see a message on the monitor telling you what the problem is (you can do this if the ? is flashing)
Also, I bought a book Nikon D3100 Digital Field Guide by J. Dennis Thomas that goes beyond the manual. Got it at Barnes & Nobel for $20. It's been very helpful.
If you have been taking photos of different subjects in different lighting, etc. and this keeps happening - well that makes me wonder. You could go back to the place you bought it and ask if they would try to take a picture and see what happens.
Good luck!