I need some advice about that too! My arms are big and they are also the weakest part of my body! I need to know what I could do to strengthen and trim my arms up!
I have recently asked for advice about this and got some good feedback from a gym instructor. Firstly, he told me boxing is a good way of firming your arm muscles and it helps to burn any excess fat that has built up in that area (providing you throw in a few upper cuts etc!). Obviously you don't need to get in a ring, but punch bags are a great way to really test yourself and if you're feeling bad about something, it's a good way of getting out your anxieties. Another one is using weights (2kg), feet apart and knees slightly bent and just bringing the weights up from in front of you and up to your chest - if that makes sense. Hope some of this helps, I've just started trying it and it's great fun - didn't expect it to be fun in the slightest!
Doing push-ups is a great tip. I can say from experience that even modified push-ups (on your knees) work great! Triceps dips are also wonderful! Try the "Bench Dip" exercise here at burn.com, it will make a big difference fast. Another great exercise for your arms (and whole body) is side plank pose: http://yoga.about.com/od/yogaposes/a/sideplank.htm. As far as using free weights, I would stay mainly within the 8 to 12 reps range and up the weight in steady increments if you can easily do more than 12 reps. Muscle is created in response to challenging/shocking the body and then allowing the tissue to repair itself. So don't be afraid to pick a weight that allows you to do 8, or even just 6 reps and not one more, and carefully work your way up from there.