Do me a favor and sign your name on a piece of paper. See how quick and easy that was? Now try to slowly duplicate that signature. Not so easy. The reason is, you're thinking about it and not tapping into your subconscious, the way you did when you signed the first time. Putting is no different. The best putters see their target line and then roll the ball on that line, just like you saw the paper and then signed it. The lesson is, keep it natural, and don't let yourself get bogged down by anything.
With the help of my sons, Ron and Dave Jr., I've developed a philosophy that focuses on this notion but also incorporates basic tips for improving your setup and stroke--the same tips I've given major champions like Phil Mickelson and Yani Tseng. Our method might really differ from what you do now, but it's the most effective way to roll the ball into the hole.
If you shot a free throw with your right hand only, you'd realize you need your left hand as a guide. The same is true on the greens: The left hand is the direction hand, and it's just as important as the right. Practice putting left-hand-only (right), or have someone hold a club in front of your hands on the target line. Bump the grip with the back of your hand, not your fingers, like Dave Jr. is doing.
The key to distance control is to roll the ball, not hit it. To do this, take an open stance, your weight slightly favoring your left side and your putter shaft leaning toward the target. The open stance makes it easier to feel the left hand going out and down the target line. The forward lean offsets the 4 degrees of loft I recommend for a putter and helps the ball roll smoothly.
When you make the stroke, keep the putterhead low to the ground past impact, like Ron is demonstrating (inset). The putter will ascend slightly, but don't try to hit up on the ball -- whoever told you to do that was wrong, because it makes the ball hop.
Grip the putter any way you like, as long as it doesn't hinder your left hand's role in the stroke. But make sure to grip the club in your fingers. The shaft should run up the lifeline of your left hand for clubface control, but your fingers must contact the grip. You can drop the right forefinger down the shaft, but don't steer with it. Forget about what your palms are doing. Fingers equal feel.
If you stare at the ball too long at address, it's easy to get brain-locked and hit a bad putt. To avoid this, I don't even look at the ball. Try looking at a spot just in front of the ball on your target line and rolling the ball over that spot. Put a tee in the ground in front of the ball when you practice (right). This gets you thinking about the target line instead of the stroke--the opposite of what most golfers do.
Another trick to free your mind is to picture the ball going in on the high side of the hole on a breaking putt. Most golfers miss low. For this left-to-right putt (below), I want the ball to enter the cup well left of center.