Anyone who's known me or really looked at this site probably knows that I enjoy science fiction a ton; and I've worked on many projects involving science fiction themes and elements; my favorite things are often set in the unknown future, Drifting and Orchestra both take place in the future, as will Project Drop Bear, and my high school notebooks are littered with drawings of various science-fiction oriented gear and vehicles. I even drew for a short while a science-fiction webcomic, and pretty much all of my animations for my graphic design class incorporated as much science fiction as possible. In short, I'm an ardent follower of everything from cyberpunk to space westerns, and though I'm not a particularly famous writer, I feel that I have a method that works whenever I want to talk about science that's far beyond what we know right now, and I've developed a simple three or four step system to avoid major faux-pas when writing.
I'm a big fan of sites like Wikipedia, because they allow me to look up cutting edge stuff and often getting lost in a voluminous archive of random information is one of the best ways to make up science fiction. I never include anything in my games or writings unless I've researched it or decided explicitly not to. For instance, the economy system in Drifting attempts to be as heavily driven as possible by what modern theory dictates about power, energy, and computing; it's built to create a scenario where the people who control tech manufacturing become powerful, and those who don't slide to the back.
I calculate everything when writing science fiction. My first advice to people whose science fiction doesn't make sense is to check why things happen. This is true for if you're trying to come up for some good technobabble to why a certain device works, but also goes a far way to explain why it was originally developed. For instance, people have no inherent need for a bigger weapon. There are only a couple reasons for arms escalation, namely that your opponent is either too heavily armored to be damaged, or is too far away or too hard to hit. Both of these played into the development of firearms as we know them, since they are powerful enough to do serious harm even through armor when properly crafted, and simple enough to use with no formal training, unlike a bow. Plus, moving a projectile at hypersonic speeds is a good way to achieve a great reach.
When I make up a concept, I try to hook it in with as many concepts as possible; one advance usually leads to another, even if there's no linear progression of science. When one use for something is discovered, the market for it rises, meaning that alternate uses are pretty common. This is why gallium is so big in Drifting, since after researching it and figuring out why it was necessary (semiconductors in a scenario where silicon is not terribly common) I then looked up other potential applications of gallium, which meant that Augustus went from just being a source of computers to being a source for all sorts of technological goodies, including applications in ion-based technology and hydrogen-related industries.
Part of what I do as a writer is look at how far things could go, but then I also take a step backward. This is sort of an optional step, but what I do is basically ask "but what would they need?" and "what could they get to?" about the people of the scenario I'm looking at. This is why Augustus doesn't have a gargantuan ion cannon drilled into the planet and aimed at everyone else while demanding tribute. Quite frankly, that technology, even if it were theoretically feasible within the stretched limits of science within Drifting, is far outside what the inhabitants of Augustus could create, so I cut it out even though the idea did pop into my head that they had a potentially brutal weapon there.
This isn't a surefire guide to great science-fiction writing, and I'm sure I'm not great, but it's a good guide for making something serious that you won't look back on by the time you're wrapping stuff up and find unbearably corny.