I will start off with two positions that you should know, both as the player having the pawn and as the other player so you know what to aim for in both cases.
Note the difference between those two positions. In the first one white can move his pawn giving a check, in the second one he can move the pawn without giving a check.
The first position is a draw and there is nothing white can do about that if black plays correctly. Thus this position, with white having the move, is the one you should go for if you are playing black.
The second position is a white win and there is nothing black can do about it if white plays correctly. Thus this position, with white having the move, is the one you should go for if you are playing white.
I can follow up with some variations in a later reply, but for now I will just post these two positions and let you have a look at them. You can try out yourself moving around with the pieces. Note that if it was black having the move then the results would be opposite, since the diagrams would swap.
Can anyone tell me the drawing,winning and losing positions in a game with King+pawn vs. King? Diagrams appreciated