The putter is a unique club in the golf bag, as it is not required to swing through nearly as large of an arc as the other clubs. Because the range of motion is so much smaller, a different grip can be applied to the putter that helps to maximize the control over the club throughout the putting stroke.
The key to having proper grip on the putter is to understand that there is no universally "right" way to hold a putter. There are many different styles of putters and different grips to hold those different styles, and a player should find the style that works best for his game and work with that grip. A consistent putter is a successful putter, and the only way to develop consistency is to find a putting style that you like and to practice until you are comfortable with it.
One of the ways that golfers choose to alter their putting grip while still using a standard-length putter is to change the position of their hands from their standard golf grip. A small change can be made by simply separating the hands slightly, so that there is a gap between the two hands on the club's grip. Some players go farther and actually reverse the positioning of their hands, with their rear hand at the top of the grip and their lead hand below it on the grip.
Players also alter their putting grip by changing the way their hands are holding the club. Changes such as this can be minor, such as the reverse overlap, where the index finger of the top hand is placed in the groove between the bottom hand's pinkie and ring fingers, as opposed to the bottom pinkie atop the top index and middle fingers. Grip alterations can also be more noticeable, like the claw grip, where the bottom hand does not wrap around the club, but instead points down the shaft.
Belly putters add an extra element of control to the way that a player holds a putter by extending the shaft of the club up past the player's hands on the grip. The end of the putter nestles against the player's belly to provide a fulcrum for the arcing motion of the putter. To grip a belly putter, players usually use a grip similar to the grip they used when holding a standard putter.
A long putter calls for the most drastically different grip of all. The putter is long enough to reach all the way to the breastbone of the player using it. To secure the putter at this point, wrap a hand around it near the top of the grip, usually the lead hand, and hold the putter firmly against the chest. Use the second hand to grip the putter down near where a standard grip would dictate, and use only that hand to move the club back, then through the ball.