I taught Logic as a Philosophy course for many years. In teaching how to work Logic proofs (similar in process to Geometry proofs), one of my best tips was to work forwards and backwards in conjunction with one another. What is your starting point? What are your options from there? What is your ultimate goal? Working backwards from there, what options do you have?
A maze-puzzle is a good illustration. Start at the beginning; when you get to a place at which the next "turn" isn't obvious, stop. Then go the end of the maze; work backwards from there until you are "stumped." Now, see what the options are for connecting the two partial paths.