I think the present and past tense equivalent in English unfortunately both translate to "你認識(或知道)他嗎?". If you are asking a person whether she knew someone prior to the time you asked the question, then use "did you know her?" This implies that the person you are asking the question currently knows the person you are asking about. 你(以前)認識他嗎? If you are asking a person if she knows about someone both now and in the past, then use "do you know her?"

"Do you know her" is present tense, "Did you know her" is past tense. In a sentence, "Did you know her before?" and "Do you know her now?"

Do is present and did is past.