Tip 1: Look at placement and shape of the green.
The shape and placement of the green will give you important hints of how your ball will roll. Does it slope away from the ball or toward it? Does it have a side hill? Is it close to a pond? How close is the clubhouse?
The clubhouse is almost always on a higher level than the rest of the course. Taking into consideration all of the larger elements of the whole green will take precedence over smaller breaks. Your knowledge of how the ball will roll starts with the information you get by looking at the overall green.
Tip 2: Check the grain of the green.
Read the grain. Grass will grow in predictable directions - you just have to know what to look for. Grass will usually grow to the west, toward the setting sun. This is good information to factor into your game late in the day. The green will slope to the nearest water area. This is especially true for courses near the ocean.
Water flows down, so slopes the land, and so grows the grass. Conversely, if your playing a mountain course, the grass will grow toward the mountain. Check the ruffled side of the hole; the grain will always run toward that direction.
Tip 3: Figure in the distance and speed.
Walk the distance from the ball to the hole and figure out approximately how many feet between them. Usually each foot between the ball and hole will need one inch of backswing from the putter. Watch for elevation changes between your ball and the hole.
The targeting of the ball will also change with the elevation of the slope. On uphill putts you should be hitting the ball with enough speed to reach a spot a couple of feet further than the hole. On the other hand, on a downhill putt you should hit the ball as if you're trying to get it to stop at a mark that's a few feet short of the hole.
Tip 4: Sight the ball.
Squat behind the ball. Find the line of your putt. Look for the high and low sides of each putt, then walk to the low side and look at the slope to check how high the slope actually is. Remember, the ball will curve in this direction.
This is very important when the ball is closer to the hole, because your putt will be much slower and will be more exaggerated by the break. If there is going to be a break close to the hole, the ball should go in the side of the hole instead of the front of it.
Tip 5: Be confident.
Simply align yourself and your putter and get comfortable. Look at the hole one more time, then make your stroke based on everything you've learned.
Practice these tips regularly and you will find your putting game improving and your confidence level rising, making your favorite pastime more enjoyable each time you play.