How is the distance between stars calculated?
You can calculate the distance between a star and our solar system, from there you can use the distance between two known stars and earth and use their location in the sky to find their distance from each other.
To find the distance from each individual star you begin by how much a star appears to "move" through the sky after a period of months. After getting the angles, called the parallax (p on the image below), you can use trigonometry to find the distance between the sun the star. The trigonometric function would use the angle p and the distance between the earth and sun, 1 astronomical unit.
After doing this for both stars you can then use the differences in right ascension and declination and apply those numbers to the distance, in a way making a three denominational triangle using the distance between each star and earth and the corresponding angles to find the distance between the stars, once more using trig.