Green is the putting area, yes.
And Par 3 means you should expect to get the ball in the hole in 3 shots or less. Par 4 is 4 shots, and Par 5 (the max) is 5 shots. Anything less than par subtracts however many under par you are from your total score, and anything over adds.
So on a Par 4, if you get it in in 3 shots (a birdie, 1 under par), you would score a -1.
If on a Par 5 you get it in in 3 shots (an eagle, 2 under par), you would score a -2.
If you shoot a 4 on a Par 3 (a bogey, 1 over par), you would score a +1.
You round score is the sum of total strokes, or more often for competitive sims and such, the sum of + and - strokes. In the above example, your score would be:
-1 + -2 + 1 = -2
Make sense??