The Elegant Universe is definitely a good thing to read, though it might take more than once to get going. And, IIRC, what you're looking for is about a third of the way through, though I'd recommend not skipping ahead because the subject builds on stuff from the beginning of the book. But Greene goes into Einstein's Relativity near the beginning, which might help you get your head around how space works. Black holes are also something to help, because they deal with gravity, which has an awful lot to do with warping of space, space tears, and (probably) parallel universes, timelines, what-have-yous. You probably don't want to call them dimensions, though, because if your book is based on physics theories, dimensions are actually directions of existence (height, width, depth, time, etc.), not parallel universes.
However, before reading
The Elegant Universe, I recommend checking out the Nova series on DVD. If your library has it, that's awesome. I started Greene's book once or twice, but didn't really get it until I had that TV visual to help. Then most of the stuff clicked.
Other than that, there's a
Physics Forum that you could ask questions on. I warn you: the people who frequent that board have a little bit of practice with the tech-speak, so you'll have to explain yourself and get them to put it in layman's terms if you're just starting out on the subject.
Other than that, you can try us here. I'm better with time than parallel universes, but I've read up on some stuff on the subject, and I know others have, so we might be able to help.