You'll get the ball closer to the hole and be in a position to drop many more one-putts, to save par (or even make a few more birdies), if you can master two simple chip shots – the high-soaring, soft-landing shot and the low "sticker" shot.
These two shots have some things in common, as well as a few differences.
First, the lower body must be kept very still and well-grounded, while the upper body rotates fully, with the shoulder coming right under the chin. Both of these chip shots require the club to connect with the ball at the bottom of the swing arc, so it's critical that you are on a solid, firm base (i.e., feet planted, lower body still).
Second, the ball has to be positioned at the bottom of the swing. Regardless of whether the ball is back in your stance (low "sticker") or toward the front (high, soaring shot), the club hits the ball at the point were the downswing stops and the follow-through begins.