For upper arm size you need to work both the biceps and the triceps, and do so properly. I have compiled two of what I believe to be the most effective exercises to build both of these muscles.
Biceps
Barbell curl: Using a straight bar with a grip of shoulder width or slightly wider, lower the bar to the bottom range of motion without letting the elbow go straight (this keeps the tension on the biceps.) Now, with your elbows tucked into your sides, allowing them to slide slightly forward during the up-movement, lift the bar up, give it a squeeze at the top, and then lower slowly.
Incline Dumbbell Curl: Set your bench to an incline, and holding two dumbbells whilst laid back, curl them up simultaneously and slowly lower. But, whilst you curl and lower, do not twist, as you might during the traditional dumbbell curl. Most people perform this exercise with a twisting motion but I believe this takes the biceps out of the exercise somewhat. Try it with the palm supine constantly and you’ll see just how much this hits the biceps. (Don’t expect to be able to lift even a fraction of what you do normally – this method of curling is a whole different ballgame.)
Triceps
French Curls: Quite often confused as a lying tricep extension (or sometimes performed on an incline), the French Curl is by far the best exercise for tricep development. Lying on a flat bench, using a straight bar or an EZ-Curl bar, with the palms facing upward underneath the bar, at shoulder width or slightly wider, triceps pointing slightly behind the head, use the power of your triceps to lift the bar until the elbows are locked out, with the bar pointing upward behind your head. Remember, the idea is to keep the stress on the triceps at all times, and because the upper arms aren’t vertical but behind the head, this takes the stress from the elbows and places it on the triceps. Now lower… slowly. And that’s a French curl.
The difference between French curls and lying tricep extensions is with French curls the angle at which your upper arm points means the stress is always on the triceps, whilst with lying tricep extensions the bar is brought vertically above the head, in line with vertical upper arms.
Skull Crushers: Another favourite of mine. Skull Crushers are performed seated, with the use of a single dumbbell. Load the dumbbell up with weight, and using your palms to create a diamond-shape grip around the bar and under one end of the plates, lower the weight behind your head, keeping your triceps vertical. Now, using triceps power, lift the weight until the arms are locked out, and lower slowly. The trick here is to not allow the arms to lock out at the bottom but stop before full extension to keep the strain on the triceps.