Most amateurs should pay closer attention to the speed of their putts. Speed is more problematic than direction, and getting it wrong is the cause of most three-putts. Here's a drill I modified from one used by performance coach Rick Jensen.
Pick a flat putting line and lay a flagstick or club two feet behind the hole. Just to the side of your line, place a tee in the green every putter-length; go back six tees, about 18 feet. Your course is now set up.
Start with three balls at the tee closest to the hole (above). Your goal is to make the putt or end up in the "safety zone" between the hole and the flagstick. Once you do that with all three balls, go to the next tee. If you leave one short or hit the flagstick, you have to start over.
After five minutes, go back to the first tee with only two balls. Same rules apply. After five more minutes, repeat the process with one ball. You'll start to feel some pressure and mental fatigue. In this third stage, go through the pre-putt routine you use on the course. Your focus will sharpen, and so will your speed control.