We read about distances to stars but how do we know? What’s cool is how simple most of the techniques are–requiring little more than the willingness to look at the stars at different times of the year. After those curious humans figured out how fast light travels, and how reliably it travels that fast, they started applying straightforward measuring methods.
There are dozens of measurement methods that can be used based on distance and situation. Some celestial phenomenon lend themselves to easier reads than others. Here is a good article that covers this Cosmic Distance Ladder.
The Easy Stuff: Nearby Stars
The Cosmic Distance Ladder is the toolkit of overlapping measurement methods used. But the most reliable method works for nearby stars and is easy to understand. Overlapping measurements improve accuracy since some methods, in some conditions have an error of +/- 25%.
Methods and technology improve accuracy over time, too.
The video below makes it clear how we use parallax to figure out how far the closest stars are. The basics are looking at the star as earth moves around Sol.