"How do you know her?"
Translation:Làm sao bạn biết cô ấy?
There are two ways to say "how?", but besides the order in which they appear, they seem to me to mean roughly the same thing.
Would "bạn biết cô ấy như thế nào?" be correct as well, or would that pose more of a question like, "how do you [do the action of getting to] know her?"
"bạn biết cô ấy như thế nào?" is literally correct. However, it sounds unnatural and carries a "word-by-word" feeling. "như thế nào" is used for "how?" when you ask for an instruction to do something (a math problem, operating a machine, etc). It focuses on methodology.