I would agree with Trebs: if you want to start understanding sci-fi, then Asimov is the way to go. the man knew his stuff. There are also a few Kurt Vonnegut titles which you might find interesting (personally I am a big fan of Cat's Cradle).
For more recent and very heavy sci-fi you could try Iain Banks, who was a wonderful, wonderful writer. Personally I like his dark fiction stuff as Ian Banks, but his sc-fi is very good.
For what I call "non-sci-fi-friendly-sci-fi" I point in the direction of the Anne McCaffrey Dragon's of Pern series, a set of books which introduce sci-fi elements slowly as not to scare the reader. Like JamasSavik said, it looks like magic at the beginning and then it is explained in science.
Good luck.