How do we know how far away a star is?
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A variety of methods. It all depends on how far away the star is.
[wikipedia link to the cosmic distance ladder for more info](https://en.wikipedia.org/wiki/Cosmic_distance_ladder)
The distance to near by stars can be measured by parallax. By seeing how much the star appears to move against the background over the course of the year, astronomers can use trigonometry to get the distance.
Astronomers can also match main sequence stars to the [Hertzsprung–Russell diagram](https://en.wikipedia.org/wiki/Hertzsprung%E2%80%93Russell_diagram)
Comparing the apparent magnitude (how bright it looks from Earth) of the star to the absolute magnitude (how bright it would be 10 parsecs away) of that star, astronomers can estimate how far away it is in reality.
Further out astronomers use standard candles. These are objects with a known brightness. By measuring the brightness of the object in question and then comparing it to a standard candle, the distance can be measured using the inverse-square law.
Type 1a supernova are useful for measuring the distance to far away galaxies. They always explode with the same magnitude so by measuring the brightness of these explosions in another galaxy, astronomers can measure the distance.
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