One way to say a galaxy is moving in a expansion is that: "their lines were shifted to long wavelengths(to lower frequencies). If the redshift was due to the Doppler effect, they are moving away from the Milk Way, at speeds of up to a thousand kilometers per second". If its line is blueshifted it is moving toward us! But just Andromeda is moving toward us and the others galaxies are receding from each other in all directions!
If the universe is finite we will see the night bright and blue. If the universe is infinite the night would be bright, because is light forever!
But, the sky at night is dark, it means, the light coming from the infinity, is finite, its not have enought time to get here and bright the sky. The expansion of the universe was so fast, that light from other galaxies was overwelmed by the expansion!