This isn't a video game, where the green is just a colored background. Various greens have different physical characteristics, and you have to understand and compensate for how texture, topography and moisture will affect the speed and direction of your ball as it rolls toward the hole.
As Eric Alpenfels, Cary Heath and Bob Christina advise in their book "Instinct Putting," you should start evaluating the green while you're approaching it on the fairway because you've got the best perspective on the topography from a distance. Keep in mind that greens usually have what is called the "architect's slope," which enables them to drain quickly after a heavy rain. That generally means that the green will slope toward the fairway.
If your approach shot lands to the left of the hole, your putt will break from left to right. If it lands on the right side, it'll break from right to left. Short of the hole, you'll have an uphill putt, but if your ball lands beyond the hole, you'll be putting downhill. Another important detail to watch for is the fall line, or the contour of the green. If your ball is on the left side of the fall line, it will tend to break from left to right, while on the opposite side the reverse is true [source: Alpenfels].