How does the expansion of the universe create redshifts?
Red(der)shift means increase in light or other electromagnetic wave-length. Cosmological redshift happens due to increase in distance from Earth and this is attributed to expansion of our universe.
Quasars that are millions of light years away from us exhibit redshift that is towards the end of the spectrum.
The distance of the far distant point-source of light increases in accordance with the rate of expansion of our universe.
In astronomy, all phenomena are interrelated. The phenomena of redshift and expansion of universe is an example. Each is attributed to the other.
Reference: wiki page on Redshift.