In a nutshell the doppler effect. Just like sound, light is a wave, when a wave is coming at you the pitch sounds higher, with light it blue shifts. When moving away from you light red shifts.
They use type 1a supernova as a consistent light source across the universe to measure this. That is because type 1a supernova are the brightest type of supernova and they are consistently the same luminosity. So known light source plus red or blue shift and a bunch of math I don’t fully understand and they can calculate with great precision how far away the supernova is and how fast its moving away from us.
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