Q:  How can astronomers measure the radial velocity of a galaxy?

        Send the light from the galaxy through a prism or a 
        diffraction grating to break it into a spectrum;
        then, measure the wavelengths of absorption or emission lines
        in the spectrum.  Use the Doppler shift of those lines
        away from their rest wavelengths to determine the
        radial velocity of the galaxy.

        It may require a big telescope to gather enough light
        from a faint galaxy to do this, but it's pretty
        straightforward.  



  Q:  How can astronomers measure the distance of a galaxy?

        Um, er, this isn't so easy.  Galaxies are so far away
        that we can't measure the parallax to them directly.
     
        If we could identify some star in a galaxy which had
        a known ABSOLUTE MAGNITUDE, then we could compare the
        absolute magnitude to the apparent magnitude and 
        calculate the distance using

                  (m - M)  =  5 log d  - 5