The Old Way
Swing your putter back and through with your shoulders.
The New Way
Keep your right shoulder in the same position it was in at address.
Why It's Better
Start thinking "shoulder stroke" and you'll find yourself opening up through impact and cutting across the ball. But if you keep your right shoulder in place, your right forearm and right hand (along with your putterhead) will move straight down the target line. When you see Tiger putting with just his right hand on the club, he's ingraining this move.
How to Practice It
Assume your putting address position and then place your left hand on your right shoulder [photo, below]. Make your stroke and use pressure from your left hand to keep your right shoulder from moving out on your forward stroke. If you do it correctly, you'll feel like your right shoulder drops slightly toward the ground through impact. Hold your follow-through and put your left hand back on the grip. Remain in this position for a few counts to ingrain the feel of a proper finish.