The phrases "want to" and "would like to" are actually interchangeable. Their usage will actually depend on the context of your statement. If you want to sound more polite (not too much imposing), you should use "would like to."

It is used when asking someone for something, and is more polite than 'I want'

"I would like sth or would like to do sth" has the same meaning as "I want to,,," but is a little more polite.

I would like......(E.g. to play, a cup of tea, etc.) Would you like............(a piece of pie, to watch a movie, etc.) If you would like, we can......(have tea, go see a game, etc.)

Correct me if i wrong, but i think that "WOULD LIKE" construction usually uses when speaker wants to express his own wishes or preferences (or ask somebody), but has no guarantee implementation of the planned. For example: I would like to dance with this girl (it's just my wish, the girl may reject this offer, in deed).