The bottom line with saving strokes around the green is that you have to be able to play all the alternative shots well. You have to get proficient at chipping, pitching, using the flop shot and being able to punch. There is no quick fix that will see you go from average to excellent, you have to put in the practice and know what type of shot to use in any given situation.
Pitching can be inconsistent from green to green. When it is you have to make a mental note of how you played the shot and adjust the next time you are there. Keep written notes if you cannot remember. Chipping is as much about your ability to read the green as it is in the execution of the shot. The flop shot is probably the easiest to get good at but if you use it all the time you are not giving yourself the best chance of holing the shot in many situations.
Bunker play again is about using a variety of shots depending on the lie, elevation of the green, how much green you have to work with etc. You can play punch and pitch shots out of the bunker as well as flop and full shots. Don't expect the ball to react exactly as the distance indicator says it will on every green, it wont.
Practice, practice and more practice is the only answer. That and making notes in order to learn from your mistakes. Sorry I cannot be any the more helpful than that.