1- How do you like him? --- What do you think of him?
2- How do you like this plain shirt? --- What do you think of this plain shirt?
3- How do you like going to the movies tonight? --- What do you think of going to the movies tonight?
I think they exactly mean the same thing, and can be utilized to ask listener's opinion about someone, something or doing something. Please correct if I'm mistaken.
In addition to that, I have my doubts if both structures can be used with asking someone's opinion about "someone else" or "something" or "doing something"! Please do me a favor and elaborate on them. Thank you in advance.