There's a few ways I see how to make imaginary things seem like real things.
Start rooting the unreal to something insanely real. Magicians do this first by drawing attention to a deck of cards, which is insanely normal and something everyone can relate to. A deck of cards should, in almost all circumstances, obey laws of normal physics and logic.
Draw people to the very personal way you see the world. Sometimes what you are describing is a very far out future of the world, and what you need is to describe is how you think about that world and how you came to it. If the audience understands where you come from, the logic is that they will believe where you want to go.