How did the scientists determine that the Universe is expanding? What did the method consist of?
Ir is based on Doppler shift 0f light from Galaxies.
When a train coming towards you make whistle, the sound gets compressed and the tone changes. The reverse happens when the train going away fro you do the whistling/ .This is known as Doppler shift..Same phenomenon is also applicable to electro magnetic waves..When the Galaxies are going away from us the light gets shifted to high wave length(Redf shift),).
IN 1920 Edwin Hubble studied the spectrum of several Galaxies and confirmed that they are going away from Us..He aslo found that the farther they are they move faster.
picture credit schoolphysics.ukl.