One of the toughest things about playing a new course is learning the speed of the greens.
The first thing I do when I play a new course is head to the practice green. I don't worry about making putts or even the direction I putt, but I do focus on the speed. One way to do this is to find something -- a golf club, an umbrella, even a line on the green -- and use it as a target.
Find something about 30 feet away from you and practice putting to the line without hitting the ball past the it. Try to putt the ball as close to the line or object as possible without going over.
You don't need even need a hole. Putt a few balls and you should start to develop a feel of the green's speed.