Start by familiarizing yourself with the fundamentals. If you don't have a solid grasp of the physics of our universe, you won't be able to manipulate them to create fictional models. "World Building: A Writer's Guide to Constructing Star Systems and Life-Supporting Planets" by Stephen Gillet and Ben Bova provides a good entry point (see Resources below).
Read reputable scientific publications such as "Scientific American," "Popular Science," "Cosmos Magazine" and "Science Magazine." These are often the best sources of new theories and ideas that can turn into topics for you to research.
Investigate the nuts and bolts of potential time travel systems. In order to make time travel believable, you'll need to base it on plausible scientific theories. "Time Travel: A Writer's Guide to the Real Science of Plausible Time Travel" by Paul J. Nahin is designed to help sci-fi writers develop credible methods of moving characters into the future or past (see Resources below).
Delve into the topic of extraterrestrials. In order to create a compelling alien species, you'll need to know what types of planets might support what kinds of life. Start your research with an introductory book like "Aliens and Alien Societies: A Writer's Guide to Creating Extraterrestrial Life Forms" by Stanley Schmidt (see Resources below).
Research material in new, cutting-edge fields such as quantum biology, super string theories, advanced robotics and nanotechnology. For a good overview of string theory and quantum mechanics written for the layperson, try Brian Greene's bestselling book "The Fabric of the Cosmos: Space, Time, and the Texture of Reality" (see Resources below).
Attend science fiction conventions whenever possible. This gives you a chance to meet other people working in the field, as well as fans. Both are excellent sources of ideas for research topics. The World Science Fiction Association has a comprehensive list of upcoming conventions (see Resources below).