Whether they realize it or not, most golfers utilize what’s called an "arc" putting stroke. Think of it as a miniature version of the golf swing, where the club travels away from the ball on a curved or arched path, and moves past the ball in the same fashion. Another name for it is the "inside-square-inside" stroke.
The arc stroke is different from the "straight-back-straight-through" (SBST) stroke, where the path of the putter head follows the target line back and through. (Although technically, even an SBST stroke features a small amount of arc.)
The arc stroke is considered more natural than the SBST method because arching allows the forearms, wrists and hands to rotate with the movement of the shoulders. On the other hand, an arc stroke can easily go off track if your grip, ball position and other factors aren’t in-sync. A slight miscue and you’ll fail to square the blade at impact.
There are few if any absolutes in learning and maintaining an effective arc stroke. Some golfers open and close the face several degrees on the way back and through, while others keep it more closely aligned with the target line.
As a general rule, however, the putter face should remain perpendicular to the path of the putter (not the target line) at all times. In a pure or perfect SBST stroke, on the other hand, the face stays perpendicular to the target line from start to finish.
One key to mastering the arc stroke is to release the putter through impact. Again, this action is a mirror image of the full swing, with the arms rotating the face from open to square to closed during the through-stroke. A failure to release properly, called “blocking," causes pushed putts, while releasing too soon may result in pulls.
A good drill to ingrain a proper putting release is to simply hit putts with your dominant hand (right hand for a righty) while placing the lead hand behind your back. The right hand will automatically roll over, ever so slightly, as you stroke the ball.
One final note: Though the point is hotly debated, toe-weighted putters are generally considered to work best with arc-type strokes, while face-balanced putters are recommend for those using the SBST method.