Unfortunately, chameleons aren't a "handling" sort of pet. They don't usually like it and a lot of times handling stresses them out. There are of course exceptions and stories of super friendly chams, but they are rather far and few between. I feel that it is important for a cham to somewhat tolerate handling for when necessary and it is nice for your chameleon to be used to your presence. You are on the right track with the hand feeding. That is the very best way to gain a chameleon's trust. When my cham was little, he would crawl on my hand and eat his meals from a cup. That really helped the taming process. Now that he's kind of a picky eater, he won't do that anymore, but it helped in the beginning for him to learn to crawl onto my hand.
You should always allow your chameleon to crawl onto your hand instead of grabbing him or her, especially from above. Snatching only leads your cham to believe that you are predator and he is being carried away to his doom. It is much better for him to recognize your hand as the friendly branch that feeds him and or delivers him to his free-range tree. (My cham enjoys spending time outside of his cage on his free-range tree. It's also a good way to get your chameleon out of his cage by himself. Simply set up a tree outside of his cage with a branch leading to it so he learns that it is ok to leave his cage.)
To answer you question about how often, it really depends on how well the cham tolerates handling. Some chams never leave their cages, while others love coming out. At this time, I would suggest that you only take him out when he willingly climbs on your hand (which might not be often or at all right now.) It really takes a lot of time and a lot of patience and you must gain his trust first. Good luck!