Get a patch kit and a tube that holds air (preferably an old or at least cheap one). Poke a hole in it with a safety pin and follow the directions on the patch kit. Make sure you spread the glue around in an area large enough so that all of the patch will be sitting on glue. Let the glue dry a bit before putting the patch on.

I think too many people wait until they get a flat on the road before trying to fix one. It's easier when your not under pressure and can take your time. Like anything else, you get better results with practice.

As far as other repairs go, see if your local bike shop or bike co-op has classes. Several in my neck of the woods do.