In putting, there are two basic strokes. There is the shorter, more wristy "poppy" putting stroke and the longer, more flowing putting stroke. Both have advantages and disadvantages and it's important to determine which putting stroke is best for you when learning how to putt better.
The "Pop" Putting Stroke
Long favored by the older greats of the game, the "Pop" putting stroke was used by golfers such as Arnold Palmer, Gary Player and Jack Nicklaus. These golfers learned how to putt on slower greens where using a lot of right wrist action gave the extra "pop" needed to get the ball to roll further.
These days, the greens are much faster so less wrist action is needed for distance. However, that doesn't mean that you should take out your wrists completely. In fact, I often see amateur golfers struggle terribly on the greens with distance control and direction because they try and just rock their shoulders during the putt. This takes out the more sensitive muscles in the arms which are much more capable of finesse and touch that is need on the greens.
By getting the golfer to learn how to putt with their right arm only and using their right wrist to move the putter instills a new sense of club face and distance control as they can now sense and feel the weight of the putter head swinging. While you needn't be as wristy with your putting stroke as Palmer was, adding some right wrist hinge is something the modern great players still do, including Tiger Woods (check out Tiger working on this drill here).
The "Shoulder" Putting Stroke
The idea of using just your shoulders in learning how to putt came along as an idea to help golfers struggling with the yips in putting. It is a putting stroke that allows you to take out the arms and hands and rely on the so-called "big muscles" to learn how to putt. In concept, this sounds like a good idea, but it has its own limitations.
The biggest problem with this way of putting is that takes out the more sensitive muscles in the forearms that give the human hand an incredible sense of finesse and control. If you were to toss the golf ball to the hole, you most certainly wouldn't do it by just rocking your shoulders, would you? Of course not. You would gently swing your arm while using the wrist extensor and flexor muscles to finitely control the release of the golf ball. When most golfers do this, they are shocked to see just how accurate they can be from most any distance, even if they're currently terrible putters.
How to Putt - The Perfect Putting Stroke
In the end, the ideal putting stroke is the one that COMBINES both these movements. You need some wrist hinge to provide the finesse and you want to use the bigger muscles to "power" the stroke. This is the ideal way to putt as it gives you the benefits of both worlds.
So, if you're struggling on the greens and trying to figure out how to putt better, check out this "How to Putt" video and learn all the keys to how to make more putts!