How would you know.... is a question asking for the evidence that you would need to make that decision. I would know that a spider bit me if... I saw a spider near or on me and saw a red mark or felt a sting. I would know if I was allergic to something if... I used it on more that one occasion and had a reaction such as hives, swelling of my face or tongue, a rash, a runny nose, watery eyes etc.. You need to have an exposure to an allergen at least twice to have an allergic reaction. If I pet my cat and then touch my eye, it will become itchy and watery... I have an allergy to my cat.

The MEANING in this is not grammatical, it's contextual -- based on pragmatics (what is going on in the conversation) "How would you know?" is usually a slightly sarcastic reply when you want to reject what someone has said. For example: A: It must be hard that your girlfriend dumped you... B: How would you know? Have you ever been in love??? or White-skinned person: Racism sucks. Black-skinned person: How would you know? or Person from rich country: These are tough times... Person from poor country: How would you know? As you can see, it's used to say "your experience of XYZ is not valid here" or "I don't think your experience of XYZ is enough / relevant" ... the meaning transcends the grammar -- you have to look at the functional purpose of this phrase to get the connotation. If you understand the connotation (not just the grammar) then you will recognize future situations / contexts you might want to use it in.

The question puts forth a possibility - a 'hypothetical' question. If A happened what would be the result? OR If A happened how would it affect B? "If you were the last man on earth, how would you know?" - this question just poses a though problem - one that doesn't really exist, but asks you to examine the possibilities. How would the last man on earth know that that was the case. He could really only prove for certain that he was the only man he could see still existed. Beyond that, he might feel lonely, but not be able to prove he was totally alone.