Roddenberry's way of thinking was that a cowboy wouldn't stop to explain to the audience how his gun worked, and a beat cop wouldn't stop to explain how his car worked, so the Trek characters didn't need to explain how warp drive worked.
So you have to look to behind-the-scenes material for warp theory. The first time it was really delved into was in NASA propulsion engineer Dr. Jesco von Puttkamer's notes for Star Trek: The Motion Picture
, on which he was a consultant. His memo on warp theory is reprinted in the book The Making of Star Trek: The Motion Picture
by Susan Sackett and Gene Roddenberry (Wallaby Books, March 1980) -- and it bears a striking resemblance to the theoretical "warp drive" model formulated by Dr. Miguel Alcubierre in 1994. A somewhat different explanation was presented in the Star Trek: The Next Generation Technical Manual
by Rick Sternbach and Michael Okuda (Pocket Books, November 1991). Since they were TNG's main technical consultants, their book reflects the assumptions about warp drive and other Trek technology that the writers and producers of the show were using (except when poetic license dictated otherwise), and has been the standard model ever since.