@George,
Thanks George.
It sounds like you're trying to gain muscle size (as opposed to strength or endurance).
You will grow muscle in your arms if you do arm exercises and eat more food (eating more food is very important). If you're looking to gain arm muscle
really fast, you need to work out more than just your arms. Your body does a better job building muscle when it is building for your entire body as opposed to just building muscle for your arms.
If you only want to build arm muscle though then the workout is really simple. You need to do exercises that work out your bicep and tricep muscles. You need to do this workout every other day (doing it 2 days in a row will slow down your progress, don't do it).
Regular Bicep curls (either dumbell or bar)
4 sets x 8 reps with as much weight as you can lift 8 times. It should be impossible to lift a 9th rep (this may require you reducing the weight each set). There should be 1-2 minutes in between sets.
Hammer curls (must be dumbell)
4 sets x 8 reps with as much weight as you can lift 8 times. It should be impossible to lift a 9th rep (this may require you reducing the weight each set). There should be 1-2 minutes in between sets.
Tricep pushdowns (cable exercise)
4 sets x 8 reps with as much weight as you can lift 8 times. It should be impossible to lift a 9th rep (this may require you reducing the weight each set). There should be 1-2 minutes in between sets.
Skull Crushers (use a bar)
4 sets x 8 reps with as much weight as you can lift 8 times. It should be impossible to lift a 9th rep (this may require you reducing the weight each set). There should be 1-2 minutes in between sets.
Close-grip Bench press (use a bar)
4 sets x 8 reps with as much weight as you can lift 8 times. It should be impossible to lift a 9th rep (this may require you reducing the weight each set). There should be 1-2 minutes in between sets.
This is what I would do; but your milage may vary. And keep in mind that this will only work for 8-12 weeks and you'll need to find a different program.
I have a lot more advice if you're thinking about starting a whole body program (which I would recommend).
Oh yeah, since it can't be said enough, you have to eat more food in order to gain muscle (assuming you're not overweight). If you lift weights and do not eat more food, you will not gain any muscle and all your efforts will be wasted.