Answer:
Well, it varys my friend and depends on a number of factors. I'll go through the most significant of them.
First factor. How much dedication and devotion you're willing to put into muscle training. Some people train a mere once a week and that one time being very non-beneficial with no effort put into it. Others might train twice a week, and more dedicated people will go into three times a week. Three is a max. You should always leave at least 2-3 days between each muscle training session as to not exasperate the muscle. The muscle does not grow during training, it grows in the recovery stage after training when your muscles feel sore, therefore, you must wait between each muscle training session at least 48 hours.
Second factor. Your diet. Are you taking in too many fats? How about carbohydrates? Do you take in enough protein? That's the question. Dieting or keeping a well-balanced meal regime throughout the day is just as important as muscle training. You need to take in alot of protein, of course, not in extravagance. Too much of anything is bad. Try not to take in too many fats, fats are never good for you. Carbohydrates are a must, but again, don't take it extravagantly.
Do the good examples I mentioned in the above paragraphs apply to you? If they do, you're on the right track my friend. However, I can't give you an accurate answer. It's an estimation, I'm afraid. It'll take anywhere from 1-2 years to put on your first 20-25 LBS of muscle. So assuming you follow the instructions/examples, you'll get a noticeable amount of muscle in your arms within 3-6 months. Don't be discouraged, it's not a very long period of time and it'll fly by before you know it. Just stay motivated, observe other body builders who did it just like you want to right now. Never give up.
Good luck.