One way to look at a putt is to be a spot putter.  Spot putting is when you pick a spot near the hole and attempt to roll the ball to that spot.  When you are rolling a longer putt, you pick a spot on the green where the ball starts to break towards the hole.  Pick a spot on the green other than the cup, i.e. an old ball mark, etc., and line up to it.  With short putts, I recommend picking a spot on the back part of the hole to roll the ball to.  For example, for a right to left breaking short putt, you can pick a spot on the right side of the back of the cup.  Unless the slope is severe, don't aim a short putt outside of the hole.  Spot putting helps to take the anxiety out of short putts.  This will allow you to focus on a small target and not worry so much about getting the ball in the hole.  Use the alignment aid on your putter and make sure it is square to the spot you are choosing to roll the ball over.  The mistake some spot putters make is they will stand over a putt and aim at the hole instead of the spot they had originally chosen.  So, look and aim to the spot you are trying to roll the ball over.  Roll the ball towards the spot and follow through with the putterhead moving toward the selected spot.