Sometimes the usages are different, as in Emily's example, but sometimes they are nearly the same, for instance: let me see = let me look at it (let me have a look - here "look" is a noun, though).
In 99% of cases, look at means something roughly like try to see, make an effort to see, direct your powers of sight toward, attend visually. In comparison, see is relatively lacking in effort. (There is no form see at.)
When you look at something, you actively do something. You pay attention with your eyes. When you see something