Scientists look at groups of stars to determine the ages. As another poster already said, the HR diagram is the tool used to determine ages. The colors emitted from the stars is also used to determine ages because color is indicative of where the star is on its life cycle.
How to Learn a Star's True Age
As the article says, stars are assessed by clusters. The stars formed around the same time and from there scientists determine the age. We have the following going on: brightness, color, and clusters. Size can be used as a determinant, however there are white dwarf stars which are very small, are dim as observed from Earth, yet are very old stars.
Also to clarify-- just because a star is far away and therefore can take thousands of light years for the light to reach is does not mean it's old. The speed of light is simply a measurement of time of travel.
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