Good question! These verbs are very close and are sometimes used interchangeably. I will try to explain them more clearly for you.
To see is to use your eyes to notice something, (basic vision): "I see a monkey." (The monkey is in your visual path.)
To look is to direct your eyes in a specific direction to observe something: "Look at that monkey!" (I am directing you to specifically focus your eyes on the monkey.)
To watch is to purposefully pay attention to something using your eyes: "I like to watch the monkeys in the zoo." (I pay close attention to what the monkeys are doing for a period of time.)
I find that this dictionary usually defines words in a clear and direct manner: http://www.merriam-webster.com
Hope this clears it up for you!