So, you want to train your triceps, delts (shoulders), biceps, and upper back.
Bicep curls you must know how to do. Do them with free weights, the machine s*cks. Start with 5 pound dumbbells in each hand and do them SLOOOOOOOW. Even SLOOOOOWER back down than up. If 5 lbs. is too easy after 5 or 6 reps, go heavier. Do 2 sets of 15 at a weight where on the 15th rep you feel like you can't use your arms anymore.
Triceps - again, I don't like the machines. Lie on your back with a weight in each hand, hands straight up to the ceiling, directly over your shoulders. Lower the weights down towards your head so they are parallel to the floor, as if your elbow is a hinge. Stop at the 90-degree angle. Raise them straight up again. Again, go slooooow, and do 2 sets of 15. This shows you how, but try not to go down so low; it's hard to keep your wrist at a good angle:

Your shoulders are actually 3 muscles, and you need to work all of them. The overhead press machine is good for that working your front and middle delts, but again, these can be done with dumbbells too if you prefer (which I do! You get a better range of motion with free weights than machines).

Machines are actually best for rear delts, but there aren't any machines solely dedicated to them. There's the upright row machine for your back that has horizontal handles too, which if you use, you get your rear delts. And there's the machine that you can use for chest flyes where if you sit with your chest against the pad instead of your back and reach around for the handles, it gets your rear delts. Looks like this:
For your back - the row machine is good (sit with your chest against the pad, reach out for the handles, and slowly bring them towards you. Pause, and slowly push them back). Your back can take a lot of weight - start with 30 or 35 pounds, even if you're not in shape.
Now, get out there and get moving!
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