To begin golf game, your golf practice game or your golf putting practice; study the art of keeping your eye on the golf ball. When putting it seems to be just natural to let your eyes follow the backswing. To correct this you might turn the golf ball until the brand is on top. Then just keep your eyes on that.
When putting, think of the golf swing as a pendulum and as you move through this area, strike the golf ball with the sweet spot only. What? Huh?
How do you find the sweet spot? Hold your putter using the thumb and forefinger. You are dangling it now and letting it swing.
With the other forefinger tap the putter blade until the putter head rebounds straight back in perfect alignment. That is the sweet spot for this putter. Some players mark it.
To judge the distance of the backswing try this exercise. Use your right big toe as a guide and take the putter back to your right big toe.
Now, being consistent with your speed accelerate the club head through the ball and watch how far that ball rolls. You might try this in both wet and dry conditions. This gives you the ability to gauge from there how long the backswing should be for the putt you are facing.
If your distance is shorter, adjust for how far inside the right big toe your swing should be. Adjust outside the toe for a longer putt. Get a feel for this and you will know how far to take the putter back.
Again, it is a feeling. Accelerate through the ball and make sure your follow through is longer than your backswing. Concentrate on feeling the putter accelerate through the putt.
In summary; You are trying consciously to get a feel for the art in your golf game. You will succeed. It just takes practice.