When practising on the putting green, always choose a level area, or perhaps somewhere where you'll be putting slightly uphill. It's true that a ball that never reaches the cup never goes in, but neither does the ball that goes past it.
My preference is for a putt to die at the hole. A putt that dies at the hole will sometimes topple in, whereas a putt that is struck too hard will hit the hole and spin away. The same number of putts are missed behind the hole as short of it. The cup is only one inch wide for a putt that is struck too hard. The cup is four inches wide for a ball that dies at the hole. A putt left a foot short of the hole is far easier to hole than one that runs three feet past. The main reason you leave a putt short is that it's not hit squarely on the sweet spot. Feel like the ball is slipping into the hole like a mouse.
One thing good putters have in common is that regardless of their style their putting stroke is approximately the same length back and through. Try also to keep the putter head low to the ground and with short putts, concentrate on the line. With long putts, concentrate on the distance.
As an old-fashioned coach -- l like a putting stroke that uses the arms and wrists. But on a very long putt, you will need to use your shoulders and take a longer backswing and follow-through. Play the ball off the left heel and place your feet square to the line.
Out of Bounds: Have you ever made fun of another golfer so much that you feel that they should be thanked for all the good times you've had...