The great thing about boxing gyms is that you can go every day for as long as you want (vs once/week for most martial arts classes) and if the guys are good to the kids like they are at my gym, they'll work with you on something new every time you go.

I don't think there's any true way to hit a heavy bag. You just hit it. I've seen some guys hammer it and some guys work on form and footwork. And like ANF said, get handwraps to protect yourself and some bag gloves to soften the blows. After that, work drills slowly at first to develop feeling and work from there.