One of the most common putting mistakes players at all levels make is getting too active with the body. To putt well, you need to set the angles in your posture, hands and arms, and keep those angles fixed during the stroke.
For example, the amount you bend at the waist--your posture--should stay consistent through the stroke. If you straighten up just before impact (usually to look up to see if the ball is going where you aimed), you'll pull the putter up in the air and hit the ball low on the face. Those putts will tend to miss short and to the right.
An easy way to preserve your posture through the stroke is to hit the putt and focus on the spot on the ground where the ball was until the ball is in the vicinity of the hole. Doing that, you'll look up when you hear the ball go in.
When it comes to the angles in your hands and arms, the simplest way to think about this is that you don't want your hands and arms doing much independent moving. A good stroke is generated by a slight shoulder turn--not a lot of arm swing. The bend in the back of your right wrist should stay consistent through the stroke--not flatten to "hit" a putt.