There are three modes of play in Hogan's Alley. The first is like a simple carnie game. Three targets at a time come out, one or two are gangsters and the others are innocents. Within the time limit for each round, you must take out the criminals. You get points for each bad guy you hit, and you get charged with a miss for each innocent you hit and for each baddie you fail to get before time runs out. Ten misses and it's Game Over, otherwise you could go on forever.
The second game is the old classic cop training course, the 'alley' of Hogan's Alley. The same targets appear, but now they come from doors, windows, behind fences, etc. Which begs the question, why do we train cops to draw and fire against a criminal who pops up already aiming a gun at them? Anyway, same rules for hits and misses, but there may be more than three targets on screen at once, and they aren't all lined up nice and neat for you.
The third game is 'Trickshooting' in which your job is to shoot cans instead of bad guys. The can flies upward when you hit it, and your goal is to coax it into the slots at the left, without letting it fall to the ground. The points for each slot are shown, but you also get 100 points for landing on the small platform near the floor. It looks like this would be harder to do and thus worth more, I don't know what they were thinking.