From the Fringe
Golfers can use the putter when their ball is on the fringe. This is the most common spot for most golfers to use their putter when they are off the putting surface. The fringe grass is just a little bit longer than the finely cut green and it may require a firmer stroke, but the fringe is not likely to change the direction of the ball when it struck evenly and with confidence.
Golfers can use their putter when they are just short of the green and in the fairway. Many golfers will automatically take out their lob wedge or pitching wedge when they are on the fairway and they want to put it on the green from a distance of 30 yards or less. However, you can use your putter if there are no hazards--water, bunker or trees-- in your way. In fact, a well struck putter from that distance can get the ball to within 5 feet of the hole. A wedge from that spot may not get closer than 10 feet.
From the Rough
You can use your putter when you are in the rough and you are trying to put the ball back in play. You are not looking to hit the ball for distance, but your ball may be in tall grass or weeds and the fairway is just a few feet away. Instead of trying to waste your stroke by taking a big swing with a long iron or wood, you are carefully trying to place your ball in the fairway. You can do this by giving the ball a firm stroke with your putter.
From the Bunker
Study the greenside bunker before you take you sand wedge to hit the ball. Most greenside bunkers are cavernous and deep and that requires you to take the sand wedge and explode out of the trap. However, there are some greenside bunkers that have no lip and are relatively flat. In these rare cases, you can take your putter and hit the ball directly at the hole. This works best when your ball is at hole height.
Behind the Tree
Use your putter when your ball is directly behind a tree and you have no chance to advance the ball. By taking your putter and rapping the ball back into the fairway, you can put yourself in a position to hit your next shot exactly where you want it to go. When you are stuck behind a tree, some golfers will try to make a "miracle" shot by attempting to go around it, only to have the ball rebound backwards. Hitting it sideways or even backwards with your putter in order to set up a decent shot is prudent strategy.