In a nutshell: as a star ages and consumes it’s fuel it begins burning heavier elements. By examining the signs of these elements being consumed we can use that as one way of measuring the age of a star. Combine that with size and luminosity and that gives an estimate of age and time left before transition to the next phase of it’s life. There’s more to it but that’s the ELI5 version.
[Spectroscopy](https://en.wikipedia.org/wiki/Spectroscopy). The light emitted by the stars, the photons, interact with the material (hydrogen, helium, etc.) and are absorbed / re-created by it. The various colors in the light (wavelengths, bands) reveal info about the elements in the star.
And they also rely on understanding of the [nuclear processes](https://en.wikipedia.org/wiki/Stellar_nucleosynthesis) going on in stars. In order for carbon to be created / if we’re seeing carbon in the spectra, then this much pressure and temperature must be present, and you only get that in a star that’s this big, etc.
The stars are basically [classified](https://en.wikipedia.org/wiki/Stellar_classification) into nice little groups, kinda like different species of animals. You look at the colors and general shape and you can tell it’s a tiger. And you know from years of studies in the past, what a tiger is and what a tiger does.
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