Everybody knows that the major influence in hitting a putt along a selected line is the orientation of the clubface. The clubface is square the starting line at address (if you are aimed correctly), and we want to get it back to square when the putter meets the ball during the stroke.
It would also be nice if the putter was travelling along the starting line at contact, and not to the right or left of it.
An easy way to solve both problems is to rest your upper arms lightly against your torso. When you swing the putter, in either direction, let your arms stay in contact, sliding back and forth on your torso.
If your hands do nothing but hold the putter, that is, add nothing of their own to the stroke, the putter has to perform as desired.
Don’t worry, the Rules of Golf allow this. It is your forearms that may not be anchored.