The key to good putting is not seeing the line, but distance control. Think about the last time you three putted. In all probability you left one short, hit the second too far and then had to make a comebacker. Or you hit the first one way too far, left the second short and had to hit it again.
On the other hand, with good distance control, you can miss left or right and still have only a short putt for a finish.
An article by Don DeLorenzo, a PGA professional at the Gilroy Golf Course has some good tips on controlling your distance.
To this, I’ll add my own tip, which was given to me by a PGA professional friend of mine: when taking your first putt, you must absolutely get the ball within an imaginary three foor circle around the hole. If you’re putting well or if its a short putt, aim for the hole. if not, aim for that three foot circle. Your second putt will then be a short tap in.
It works. If I ever three putt, I am having a very bad day, indeed.