If you want to dive that deep into the matter ('solid-state physics'), you may well start with wikipedia ( https://en.wikipedia.org/wiki/Piezoelectricity or https://en.wikipedia.org/wiki/Surface_acoustic_wave ). Although not exactly what I'd recommend to an EE student.
Basicall spoken, the input transducer converts electrical into mechanical energy that travels down the SAW. The output transducer converts the mechanical oscillations received back to electrical signals. The 'how' is where physics starts...