How do we measure radial velocity of stars?
Red or blue shift.
Looking at the spectrum of light coming from a star, we can identify emission or absorption lines as characteristic of particular elements, but shifted toward red (longer wavelength) or blue (shorter wavelength), due to doppler shift.
You have probably heard the sound of the siren of a passing emergency vehicle change as it passes by. As it approaches you the wavelengths of sound are compressed, resulting in a higher frequency. As it recedes from you, the wavelengths of sound are stretched, resulting in a lower frequency.
A similar effect happens with light.
By measuring the size of the frequency shift we can calculate the radial velocity.