When someone makes an assertion, the distinction between "how did you know" and "how do you know" seems to be that "how did you know" implies that the person in question is correct in their assertion. "How do you know" is normally an inquiry into the person's credentials, and often expresses that the assertion is incorrect and/or ungrounded. Does anyone know what the reason for this distinction is? Why does simply changing the tense of the verb change the implication so strongly? I suspect that, linguistically speaking, the "did" might be a different tense than the past tense, but I'm not sure what it is, or I could be entirely wrong.
The changing of the tense indicates that, in the case of "did" the fact has been established as true in the past. The truth value having been set, the question is "how DID you (before it was set) know that it would turn out to be true?"
The question phrased in the present tense is a challenge -- the truth value has not been set as of right now (in the present) so the question is "since we haven't ascertained truth, how can you be sure of your assertion?"