"This is not a dream!"
Translation:Ez nem álom!
Because "nincs" means "there is no". So it would literally become "This is there is no dream".
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."
Yes, it is "there is not", rather than "it is not". It is an existential thing. Something does not exist or is not located somewhere.