Watch is something you do actively. You focus on something and observe it for some duration, or period of time. It can mean either look at and pay attention to something, or to pay attention to something to keep it safe. For example you might watch tv, and at the same time watch your children. Even though your eyes are focused on the television, you can still hear your children and you keep them in mind.
Look is also active, but it requires no length of time. You may look at something for only a second. You might look at something so that you can begin watching it. It is basically the action of moving your head and eyes to focus on something.
See is not always active. If your eyes are pointed in the direction of something, you can see it, but you might not give it any thought or pay any attention to it. Unless you specifically focus your eyes on it, you would not be looking at it either.
For example, you see the ground (unless you're looking up). However, you would not watch the ground, unless you were expecting an earthquake or something very unusual. You probably also would not look at the ground unless there was something unusual about it, or if you were nervous around another person, instead of looking at that person you might look at the ground.