Hola, Tyler. "To get to" significa "alcanzar" (fisicamente o no fisicamente). Por ejemplo: "She always knows how to get to the airport" = Ella siempre sabe como alcanzar (llegar) al aeropuerto. "She always knows how to get to me" = Ella siempre sabe como alcanzarme (afectarme/persuadirme/hacerme sentir mejor). Espero que me comprendas. Solo hablo más o menos español a lo mejor =\

This means she completely understands how he thinks and knows exactly what to say or do to provoke him (could be good or bad) If you have more of an example I can explain further. For example if I said my best friend "just gets me" it would mean she truly understands me and how I think/feel.