Some of the breakthroughs of the Xia dynasty was bamboo annals and oracle bones script.
Oracle Bones
Oracle bones were uses right and sent messages to ancestors who had passed away. They were written in traditional Chinese characters.
Bamboo Annals
Bamboo annals were used in Ancient Chinese courts, much like how we type up dialogue in courts nowadays. Ink would be put on bamboo sticks, in order to record what happened.
Because there were no spoken words of the Xia Dynasty it was described from ancient records like remains of the kings, officials and the prison conditions, ancient text, unearthed palaces, mausoleums, Bronze, and more objects. And that's how we know about this kind of history!!