First, consider the setting which is a key element. If it's a science fiction story set in a space station on the edge of a black hole, that's already very unique. Then add in elements like alien races that have adapted to live in such a high - gravity and radiation - filled environment. The characters in your story could be astronauts trying to study these aliens while also dealing with the strange physics near the black hole. You can also introduce a plot twist related to the science - fiction element, like the black hole being a portal to another dimension.
You can start with a unique scientific concept. For instance, if you have an idea about a new form of energy that can manipulate time, that could be the basis. Then build a world around it. If this energy is discovered, how would society change? What new technologies would emerge? And create characters who are affected by this new element. Maybe a scientist who discovered it but is now hunted because others want to use it for evil.
To create a unique story using science fiction elements, focus on the human element within the science - fictional world. Let's say the genre element is teleportation. Instead of just using it for quick travel, think about how it affects relationships. Maybe a character teleports away from their family without realizing they can't come back due to some unforeseen consequence. Also, combine different elements. Mix teleportation with a post - apocalyptic world where only certain areas can be teleported to. This combination of elements can lead to a very unique and engaging story.