In addition to the earlier answer, I would only add the governing equations relating surface wave phase velocity to shear-wave velocity can be found in many seismology textbooks.
Almost all the energy that propagates in the subsurface as a result of an energization occurs through surface waves (mainly Rayleigh waves). The analysis of Rayleigh waves using MASW technique is performed through the treatment of the spectral seismogram, that is a result of a double Fourier transform, which returns the signal spectrum. In this domain (transformed domain), it is simple to go to separate the signal relative to the Rayleigh waves from other types of signal.