Step 1: distances up to 100 l.y.

For near-by stars their distance is measured by parallax: the star is observed in, say, December and then in June, and the direction of the star with respect to the sun is measured in both cases. Knowing these angles and the diameter of the orbit of the Earth around the sun, one can determine the distance to the star (see Fig. 8.5).

 

Figure 8.5: Knowing the size of Earth's orbit and measuring the angles of the light from the star at two points in the orbit, the distance to the star can be derived. The farther the star is, the smaller the angles.  

As we look at farther and farther stars the angles measured come closer and closer to 90^o. For stars more than 100 l.y. from Earth one cannot distinguish the angles from right angles and the method fails.