"Next to" means "almost" in this case.
Imagine a scale of possible prices, from zero to infinity. What sits immediately next to nothing (zero) on that scale? "Almost nothing."
"How next to?" is a jocose question whose purpose is to determine the degree of "almostness": how close to zero, exactly, is the price? Does "almost nothing" mean a dime, a quarter, or ten dollars?
Closely related is the idiomatic phrase "next door to":
A rhinestone tiara she wore to a costume ball.
Next door to glass.
In this excerpt from A Streetcar Named Desire, a play by Tennessee Williams, Stella explains to Stanley (who thought that he was looking at something valuable) that the tiara is really, really cheap. "Next door to glass" means "Those are not real diamonds. They're fake. They're made of rhinestone. How expensive is rhinestone? Barely more expensive than glass."