US Army teaches point shooting with BB guns, at least that was the training they used in '71. I think today I'd use Airsoft. Much easier to see your round.
The Army used hand thrown targets. You can use whatever you have laying around, and not just sky shots either. Tie a tether ball on a tree for a swinging target. It doesn't take that many sessions to see some real improvement. It sure makes small game handgun hunting more productive.