One thing that people think about science fiction is that you have to be an expert in engineering and physics to write it. You don’t, you just need to know where the stoplights are are.
By stoplights I mean things you can’t do, or if you do you must do with forethought.
As for the laws of physics there are really only a handful you need to be wary off. This is not saying you can’t violate them, but if you do it will have a big impact on your setting and you should think about it.
The first of course is faster then light travel. I will say that technically are a few ways around this that do not violate the laws of physics, but they tend to require exotic matter (matter with negative mass) or something equally unlikely.
Also be aware that you would be hard pressed to find a way to go faster then light in the real universe that would not also work as a time machine.
The second of course is time travel. Violating causality is probably the first or second thing most scientists would say if you asked them for a list of impossible things. No plot element causes more problems, for the love of god if you use this think it out.
The third is conservation of energy and momentum. Also known as not getting something for nothing. If something is being powered, where does it get the power? If something is moving what pushed it?
You don’t have to do math but if you have a machine doing something think about the kind of power it uses and what that means. If you have a ship move half the speed of light that takes a lot of power, it does not matter what kind of drive system it uses.
Lastly try not to go against the grain of science. By this I mean make your fake science SOUND like real science. Science in its most basic form will be the same in a thousand years as it is now, the thought processes will be the same because we will still be studying the same thing (the universe).
One trap you can fall into when placing your character in a setting is making creatures and settings so alien that they are unrelateable.
The first and most often given advise is for you to give your character problems that are familiar. While good advise this is not the only thing you can do. If you’re are going to do it however, the easiest way is to stick to the basics, food, water shelter, saving a loved one, basic primal urges that everyone has.
Once your story progresses you can and should expand, but make sure before you do that that your reader cares about your character.
You could also show that he acts very human, that he makes mistakes. Basically show that he thinks like a human, maybe contrast it with someone or something that does not.
Lastly you can do the opposite, make the reader hate the enemy of your character and root for your character just because he is the enemy of the bad guy.
This CAN work, but its hard to pull this off. And for the love of god give your character at least one or two good qualities.
One thing that often is poorly thought out in science fiction books is how trade works. I don’t mean the technology but how it work economically.
Trade of manufactured goods only happens when the cost of transporting something is cheaper then the cost of making it.
The thing is that with enough technology you can reach a point where you don’t need trade or it can’t be profitable enough to justify it.
You also have to take time lag into account. If you just got to a new system, and you find it has almost no uranium, which you need to power your nuclear reactors that does not mean you can send for it. If you have no FTL travel you would have to wait so long that the whole thing would be moot.
You can of course have trade be only possible because things are not natural. For example if only the home planet of an empire is allowed to mine and refine uranium then they could trade, even though it would not normally make economic sense.
Think about how trade works in your setting. Why certain places trade instead of making things themselves.
There are several common ways that authors have FTL work, they all have disadvantages and advantages. As always the limitations such drives have are just as important as their strengths, if not more so.
The first is the jump drive. This allows a ship to teleport itself, not passing through the space between at all.
In the Foundation series this is how FTL works, it is limited only by star charts and how fast the pilot/computer can do the math for the next jump.
In some books that use this system the points in space that can be jump from are the limitation.
In order for this drive to not just bulldoze all your plot away you do need to use limits to your using this one.
The second is hyperspace. This means the ship travels though a different dimension, bypassing the laws of physics by going someplace the speed of light is not a limitation.
Babylon five used this method, the ships would enter hyperspace then travel using their normal drives. Then exit when they got to the point in hyperspace that corresponded to the point in normal space they wanted to be.
The third is the warp drive. This drive allows travel faster then light through our universe. This normally involves warping or creating space. Unlike the others this one can allow tracking and interception by people not traveling FTL.
All three of these have been used effectively, and it’s quite rare to find an author who uses a method that does not fall under one of those three above.
However what is more important is what limitations the drives have. In Dark Matter the blink drive can go anywhere in one jump. In the foundation series it could take days to do the math for a single jump and that jump can only take the ship so far.
I would spend more time trying to come up with interesting limitations for one of the three above then trying to think of a new way to travel faster then light. If you can come up with one, awesome use it. But don’t beat yourself up over not being able to come up with a whole new system.