A high percentage of golfers grip the putter three ways. One way is to grip it with both hands, then overlap your right hand with the index finger of your left, assuming you are right-handed. Another is adapting the so-called Vardon grip, which means you will put you hands on the grip, side-by-side, and overlap your left hand with the pinkie of your right. The third is called the "baseball grip" because you grip the club with both hands and have all 10 fingers on the club.
Some of the best players in the world have found new ways to grip their putters. Many touring professionals grip their putters "cross-handed" as a way to reduce the amount their wrists break when they putt. Then there are others who have adopted the "claw" grip. Assuming you are right-handed, place your left hand on the putter, then invert your right hand and place it just below your left, and hold the putter between the thumb and forefinger of your right hand, with the fingers straight and pointing in the direction you want the ball to go.
Longer Putter, Different Grip
Some players have purchased longer putters to improve their games, but they have had to adapt their grips to accommodate them. Some have putters that come to rest on their lower chest, creating a fulcrum. Most of them will grip the club conventionally with both hands on the grip together. But if the putter is even longer and its butt end rests somewhere near the neck of the golfer, he might grip the club at the top with his left hand to steady it, and place his right hand on the putter about belt-high.