Having a good short game will definitely help lower your scores. Knowing the type of shot to play around the greens and choosing the right club will increase the percentages of getting up and down.
Hitting bump and run shots are a good choice if you have a lot of green to work with. For a short shot with the pin close to where the green starts, you want to use a more lofted club to make the ball go higher and stop more quickly.
When you are pitching, you'll typically use a lofted club like a sand wedge. Try and match the length of the backswing and follow through. Ball position will be farther back the closer you are to the hole. For a longer pitch shot, play the ball just slightly back of the center of your stance.
Staying connected with pitch shots so that arms and body work together will improve your contact. You don't want a lot of wrist action with pitching or chipping. The wrists should stay firm in the downswing and follow through.
When hitting a pitch or chip, it's important to have the shaft leaning forward so you are hitting down on the ball. This will allow you to use the loft of the club correctly. The hands should be ahead of the ball in the setup and come through impact at the same position.