How has the doppler effect and the redshift of stars and galaxies indicated that the universe is expanding?

The effect of red shifting in wavelength is continuously increasing which depicts the expansion of universe.

Explanation:

In Doppler shift there occurs an apparent change in the wavelength of the light emitted by star

For example – If a star is near to earth, the light emitted by it would be shorter in wavelength while a star far away from earth will emit a light that has a longer wavelength.  

Thus a shorter wavelength light is shifted towards  the end of spectrum which is blue while a longer wavelength light shifts towards the red end of spectrum (known as redshift)

The farther the star from earth , the more it is red shifted . The red shift effect is continuously increasing.

Hence, both Doppler and redshift affect depicts that universe is continuously expanding.