How do we know what we know about Plato?

Good question! In the first century C.E., or about four hundred years after Platos death, all the writings that make up the canon you are reading were published by Thrasyllus, a scholar and astrologer from Alexandria that devoted much of his life to the works of Plato. Most of the medieval manuscripts that have survived derive from his collection, which is the basis for all modern complete editions. Thrasyllus transcribed Plato's work (which probably existed mostly on papyrus or sheepskin, not stone) and it is these transcripts that have mostly survived from antiquity, not the original work. Beginning with Thrasyllus himself, scholars have spent whole careers analyzing what was truly the work of Plato as opposed to what has been ascribed to him, therefore we have a pretty good idea what is authentic and what is not.