Apart from the confusion that the person asking the question doesn't usually define god the same way the person answering the question does, and apart from discussion on what know means and the meaning of means the question raises some very interesting points.
Often the questioner asking "How do you know...", "yes, but how do you know?" is really asking this slightly different question "but how can I know that you know?" or "how can I know that you know that you are not deluding yourself?" and this is often apparent from their dissatisfaction with the answers given, showing that it is themselves that they wish to satisfy that you know.
Who knows what?
The larger question we notice, is this: Is it possible for someone to know that you know that there is a god without themselves then also knowing that there is a god? I don't think so.
Or, is it possible for someone to know that it is possible to know that there is a god without also simultaneously knowing that there is a god?
More simply: Is it possible to know that a test-for-god is a valid test without knowing the results of the test?
If it isn't possible, then it may be impossible for the question "yes, but how do you know there is a god" to ever be satisfied without the questioner submitting to the test-for-god.
Of course is seems reasonable that the person claiming knowledge of god is lying or mistaken. Careful scrutiny by the questioner may reveal the lie or the mistake, but this would cast no light on the existence of a god, only on the character of the believer.
The answer of the believer is "You can't know that I know." and maybe also "but you can know for yourself."
Of course, this second point is only true if we inhabit a universe in which there actually is a god who is willing to reveal himself, and who presumably will be the one to dictate the terms under which to do this.
The deeper question
The questioner really wants to know which universe they live in: with a god who will reveal himself - or without. (It would be embarrassing to undertake the proof-of-god test if it were unreliable).
But to know that he lives in a universe with such a god is to know that the proof-of-god would work and also to know that god exists.
And if he lives in a universe where there is no such god, then he cannot be sure what a proof-of-god test would show anyway.
The place for Faith
The only way to proceed with a proof-of-god is by faith, hoping that it will work if we inhabit a universe with a god, and of course if we are trying a valid proof-of-god.
Some might suppose that in such a universe with a god with paying any attention to that a proof-of-god will find it's way to those who are looking.
Faith is how I learned to walk, why I started brushing my teeth and how I learned assembly language with nothing but a mnemonic table and some few kilobytes of lightly commented assembler listings.
I don't see why god should be a special case.
The quest to validate the proof-of-god is the quest to discover god.