At the start of a project, we haven’t set a precedent baseline of how to estimate our stories. So at our initial estimation meetings we can pick one average story as our Golden Story and give it a number (say 3). And then we compare the other stories to it: simpler might be 1, harder might be 5 or 6.
Story points measure relative effort, not hours. They should be roughly linear but stay fuzzy at first. Write the point estimation onto the story. And keep the story brief. Perhaps just a title and a few short notes.
Over the course of the project we continue to estimate, deliver, then recalibrate; this quick feedback loop is what turns our early imprecision into useful predictability.