The main muscle at the back of your upper arms is called the triceps. The best exercises you can do to tone this muscle are tricep pushups, or tricep dips, or tricep kick backs if you have a weight.
Tricep pushups : Like ordinary pushups, but put your hands directly under your shoulders with your fingers pointing out in front of you (it will feel really weird). You can do them on your knees, try to keep your pelvis flat and your bottom down but if you cant, just get as much weight forward onto your arms as you can handle and go down as far as you can. They are really hard (especially at first!) and you should feel it down the back of your upper arm if you are doing it correctly.
Tricep dips : Find a bench, sit on it with your feet flat on the floor, pointing forward and about shoulder width apart. Put your hands down on either side of you with your fingers curled over the side of the bench. Lift your bottom off the bench and lower it down in front of the bench, and then lift up (but dont sit back on the bench!) and go down again. Try to do 20 reps, but this is pretty hard when you are starting out. You should have your weight on your arms, and that's where you should be feeling the burn!
Tricep kickbacks : If you have some weights, you can try this one. You kneel on all fours and grasp a weight (you could use a can of baked beans or sometihng) in one hand. Pull that arm in by your side, with your elbow right in at your side. Moving the lower part of your arm, and keeping your elbow still, extend your arm straight back bringing your hand towards your feet. Repeat. Again, you should feel it in your upper arm. Don't forget to do the other side too!
Hope that helped a bit. My descriptions are a little dodgy, but maybe google them and see if you can find some videos or something. Or, join a gym, and ask one of the staff to show you these exercises.