Which is more correct?
How do you think about me? or How you think about me?
As referenced in this answer to another question, "Wh- words like who or when or how or why require inversion and DO-support only when the clauses they head are formal questions."
In this case, you are using a wh- word ("how") in a question, so DO-support is required, and therefore your first version is correct.
It seems very likely that you have the wrong wh- word. It looks as if you want to ask someone what their opinion of you is; that is, you want an answer like "I think you're very smart" or "You're a really nice guy". In this case, you really need to ask "What do you think about me?", or more normally, "What do you think of me?"