Good Exercise to slowly build muscle

You can make good progress at home with calisthenics and exercises that use your body weight.

If you can add some minimal equipment like a set of dumbbells your options increase.

I can't really write a program for you, I'm not qualified and I don't know your current ability.

You shouldn't neglect the rest of your body, but if you want stronger arms you will be particularly interested in things that work your triceps, biceps and shoulders. Triceps push, biceps pull. So with no free weights you're looking at probably push-up and pull-up variations. Even if you can't do a single one of either of those yet no worries. Easier variations exist.

You may find a site like this helpful. It lays out progressively harder versions of things to switch to as you get stronger. http://www.fitness666.com/p/exercise-progressions.html

I guess i should say that you may offend people who spend their lives TRYING to build muscle.

SLOW is the only way. I promise doing your first set of curls will not make you explode.

well i would approach it first by looking at your body as a whole, not part by part.

Strength training is important for every part of your body. You will be able to tell if you are over exerting yourself. Listen to your body and make smart decisions to protect your joints. I suggest contacting a professional in your area who is willing to put a program together for you, more-so who can teach you form, tempo and what to do for highest efficiency.

Wall pushups at first....whenever you have a free moment, do as many as you can. Do that throughout the day. Then when you feel comfortable, do "lady" pushups or regular pushups throughout the day. No excuses!