How has the Doppler effect and the redshift of stars and galaxies indicated that the universe is expanding?
In 1920, Edwin Hubble studies the spectrum of different galaxies and found that they have red shift in their spectra.
This indicates that the galaxies are moving away from us. He also found that the more the distance to galaxies, their recession speed is also high.
Red shift indicates that the galaxies are going away from us.
This is similar to Doppler shift in sound of a moving train.