But it seems that rarely is Hungarian translated literally but rather has many colloquialisms. I thought I was supposed to use "nincs" every time that I ran across "it is not."
nincs is more or less like nem van -- and so like van it is used in situations such as "there is [an object in a certain location]" but not in situations such as "X is (a) Y" (the cat is red, the book is a novel, this is a dream", etc.
This would mean 'Not this dream' But instead it would be ' This is not a dream' Because 'nem ez alom' will make it sound like you're talking about a specific dream rather than saying it isn't (: