I was very much like you. A skinny kid who wanted to put on some muscle. At first, I followed the hype. I got myself a gym membership, did some weight lifting, spent a ton of money of sports supplements and did not see any significant gains. I justified my purchases of these supplements because they promised magical muscle growth. They didn't deliver much.
Then I stumbled on Starting Strength. It is exactly what it sounds like. It's for people who have skinny arms, and can't bench press worth a damn. I have seen constant strength gains in all of my lifts by approximately 5-10 pounds per week. I went from barely being able to squat with a bar (45 pounds) to 160 pounds. Needless to say, that is incredible amount of growth.
It's an old school workout that revolves around three things:
proper weight training, nutrition, and rest. If you want to see gains, you need to do these three things right on a REGULAR basis.
If you have some money, I would seriously recommend purchasing his book:
Starting Strength by Mark Rippetoe
There are only a few exercises to master, however, this book goes in detail on what proper execution should be for each exercise. He covers exactly what each muscle in your body should be doing, in each position, of each exercise. The section on Squats alone is over 30 pages! I found the information in there extremely valuable. And quite frankly, if you are doing weight training, you really need to have the right form. Otherwise, you will end up doing more harm than good.
However, if you happen to be a broke college student, I would check out this post:
Guide to Novice Barbell Training, aka the Official RIPPETOE-STARTING STRENGTH FAQ - Bodybuilding.com Forums
This is a good introduction to the Starting Strength. It is very long, however, if you are serious about increasing your strength, you better read up.
Again, I would like to emphasize that you should perfect your form before you try and put on the weight. Otherwise, you're going to face some pretty serious injury.