How's a star's distance measured?

There are two main methods: The parallax method as explained above and the spectroscopic method.

With the spectroscopic you can measure far greater distances then you can with the parallax which is only aplicable to about 500 lightyears.

The main tool scientists use is called the Hertzsprung - Russell diagram. It is a chart that you use to classify the star you are looking at. You find its temperature, its size, its luminosity and its make up by analyzing the stars light. When a star is then positioned on the HR diagram you can calculate its absolute magnitude. You then compare it to the apparent magnitude and use an equation to calculate the distance. By using a type of very bright variable star, called a cepheid varible, you can use the spectroscopic method to measure galactic distances as cepheids work as kind of a standard light. Once you see one in another galaxy all you have to do is measure its period from brightest to dimmest. You then have the absolute magnitude of the cepheid. How accurate the spectorscopic method is for measuring distance varies with distance as fainter light is more difficult to analyze.

If you know something about trigonometry, you would know that if you have a rectangle triangle, knowing 1 angle and the length of one side, you can tell all other things. Parallax method uses this. If you know the distance from Earth to Sun, you can measure the angle with wich you are seing a star in 2 different moments of the year (almost all the time in 2 opposites part of the earth's orbit.) Then, you have all data needed: The length of the triangle side, and one of its angles (actually the 3 angles.)

This method only work with near objects. For far away objects other methods are used, based on the frequency of the waves that arrive from them. Usually there are markers (objects with a distance well determined) and comparing this bodies with other, it's possible to calculate distance.

There was an old method called the parallax method which you measured the same stars angulard difference between six months. Pretty much like when you look at a pencil from an outstretched arm with an eye at the time and measure the difference by calculating how much it seemingly moved.

This as I recall gives the most correct distance.