Many weekend golfers make the mistake of trying to finesse the ball into the hole from short range. Unfortunately, this often causes the ball to lose its line and miss the hole entirely. While it may seem counterintuitive, you'll make more of these putts if you hit them with increased pace—in other words, with enough velocity to hit the back of the cup.
To get the feel for the proper speed, create a barrier with a pencil and two sets of tees about an inch in front of the hole. Now roll a few putts from three to five feet and try to get the ball to barely pop over the pencil and fall into the cup. This is the perfect speed for short putts. If you baby the putt, it won't have enough speed to get the ball past the pencil or the tees. Hit it too hard, however, and the ball will jump over both the pencil and the hole. Once you get good at this drill, remove the tees and pencil. Your newfound pace should have those short putts rattling off the back of the cup every time.