"You drive for show and you putt for dough." In golf, this isn't just a cliche; it's a fact. Consistent putting will help you win more matches and tournaments than any long drive. To become a good putter, you have to learn how to grip the club.
Take the putter in your left hand as you would any other club. Take a standard overlapping grip, where the small finger of your right hand goes on top of the gap between the forefinger and middle finger on your left hand. Hold the club somewhat lightly and make sure you don't choke the club. You want each of your fingers to feel the sensation of the club underneath.
Take your normal putting grip but instead of holding your putter at the top of the grip, move your grip 12 to 14 inches down the club. This will give you the sensation of being closer to the ball--and you will be. This grip will give you greater touch when you are on the green.
Use a cross-handed approach if you have a hard time executing an even stroke. Instead of putting your right hand under your left, put your left hand under your right. This will look awkward to your playing partners and will take some getting used to on your part. However, it will help you keep your left wrist firm as you putt the ball. That will help your putt remain on target.
Turn your body so you are looking directly at the hole. Take your left hand and hold the top of the grip and drop your right hand about 8 to 10 inches below your left. Keep your top hand steady and draw the club back with your right hand and then stroke the ball with a smooth follow-through. This is called the side-saddle grip, good for golfers who have a hard time judging distance and direction while on the green.
Consider a belly putter if you feel your hands are shaky upon impact. Many older golfers believe the belly putter--a much longer putter than normal and one that extends to the golfer's belly--keeps the club steadier through the putting process and enables a smoother and more accurate putt.
Tips & Warnings
Practice putting in your house. Take a drinking glass and put it on its side in your living room. Take a putter and a ball and attempt to putt it into the opening. While the feel of your carpet is nothing like the feel of the grass on the green, it will help you develop a smooth stroke. Work on your putting on the practice green that nearly all golf courses have.