Every story begins with an idea. What's amazing about science fiction stories is, they often start with a cool idea. Like a spin on space travel or robots that nobody's ever thought of before. But how do you turn an idea into a story, with memorable characters and powerful moments? That's often the hard part.
Just the same way there are no rules for good storytelling (other than "tell a good story"), there's no right or wrong way to get an idea for a story. You might start out with a character or a cool scene, and build a whole story and concept around that. You could start with a world, and dream up the whole history of that world, before you figure out when/how your story starts and what the notion is. Or whatever.
But oftentimes, a great science fiction story does start with a high-concept idea — like, say, the first ever generation ship is halfway to another planet when we discover that the drugs we gave the colonists to protect against cosmic radiation are causing mutations, and maybe whatever arrives at the new planet won't be exactly human any more. (Apologies if that doesn't sound like a cool idea, I just came up with that on the fly.)
No matter how fascinating and inventive your basic story idea might be, it's still not a story. There's a term among science fiction writers and editors for a story that just lays out a cool idea and then ends: a H.A.I.T.E. story, which stands for "Here's An Idea. The End." At the very least, you want to have some progression in there, a beginning, middle and end, and maybe a few surprises along the way. And there need to be some people in there, to cope with the situations you've set up.
But you don't just want to do the very least — you want to create an awesome story, that will stick in people's minds after they're done reading it. And for that, you need to engage people's hearts as well as their minds. You need more than just a fleshed-out plot to go with your concept, you need some emotional hooks. Joy and pain, man. Like sunshine and rain.