Reading greens is an art that many golfers spend too little time thinking about. Spotting subtle slopes and building a picture in your mind for how the ball will roll requires some careful observations. The first thing to remember however is that, essentially every putt is straight. All you can do is pick your line and hit a straight putt to the apex of the curve. Then, depending on the quality of your read and judgement of pace the ball will either go in or it won't. Before we get into the specifics of green-reading remember that once you have picked your line, aim the putter face at the point at which you expect the ball to break. I often think many amateurs get drawn into aiming too far towards the hole when they face a big, swinging putt. Don't fall into this trap.
Over-flowing with water tip
Of course, the slower the ball is travelling, the more break it will take. That's why you need to pay particular attention to the slopes surrounding the hole. A good tip is to imagine the hole over-flowing with water - where would that water drain off? Visualising this will really help you pick out those subtle slopes that many others will miss.