Well, I'm beginning developing my first sci-fi stories ever... eep!

And (what do you know) I'm a little unsure about... stuff. Besides usual unsure-ness that comes along with every story, I really am not sure how developed the science in my story needs to be. I'm sure the exact detail requirement varies from story to story based on tone and style, but I'd still like to know basic outlines and such.
If I do need to know nearly exact workings of (at least the theories of) the techno-science, I'm in trouble. I have a parallel universe to ours in the story, centering around the twin planets of Gran and Stork. An evil scientist/wanna-be-world-ruler has done something science-y that sends any obstacles to a place where their life on Gran or Stork will only be a dream. They get sent to our world, and live as a normal person with a normal family. The only thing different is that their dreams, a good deal of them at least, are flashbacks to their life in the other universe. Only problem, I have no idea how a human on Gran or Stork could get sent to our world and live their whole life as an Earther (as Graners or Storkers call them). Do I need to know?