Redshifts can be detected in even comparatively nearby stars. In fact, redshifts, although extremely tiny, can determine if and how fast an individual star is rotating. ie, one half of the star is blueshifted, the other redshifted, meaning one half is moving towards earth (blueshifted) the other away (redshifted). Blueshifting is the shortening of light waves. Redshift, the opposite: lengthening.
As with the changing pitch of a moving car's horn, light waves can shift toward higher or lower frequencies. Higher frequency = shorter wavelengths (blueshift). Lower frequency = longer wavelengths (redshift). Blue = approaching. Red = receding.