A method for the measurement of the phase and group velocities of guided acoustic waves is presented. For this purpose, a unique capability of a self-developed double-pulsed TV holography system to create movies of the propagation of guided acoustic wavetrains is used. Thereby, the experimental visualization of the evolution of Lamb and Rayleigh wavetrains in aluminum plates is shown, including several movies that illustrate different dispersive behaviors. Each movie shows the propagation of a narrowband wavetrain with a central frequency in the order of 1 MHz that consists of a carrier moving with the phase velocity, modulated by an envelope moving with the group velocity. Each snapshot is a two-dimensional map of the instantaneous out-of-plane displacement field of the surface points of the plate, with amplitudes in the order of several nanometers, acquired with the double-pulsed TV holography system. Then, by repeating the acquisition with successively increasing delays between the generation and detection instants, a sequence of maps is obtained from which a movie is composed. The phase and group velocities of the waves are accurately measured from the movies, yielding values that match well with the reference values for the same plates obtained from independent measurements.