I've spent a bit of time looking around and found the followng. In The Rise of Skywalker: The Visual Dictionary the lightsaber has several annotations on it reading:
Leather wrist strap repurposed to bind broken shaft
Weld marks
Kyber crystal inside healed using techniques gleaned from Jedi scripture
Click image to enlarge.
Of course fixing the casing was the easy bit for Rey from being a scavenger, she just welded it back together and used some leather strapping to help bind the two halves together. However, it also seems from the Jedi scripture she took from Ahch-To was some information on healing the Kyber crystal.
We get a bit more information on this later on in The Visual Dictionary where is states the following along with an image of Rey's little workstation on Ajan Kloss:
Rey is fascinated by the arcane healing techniques described in the Chronicles of Brus-bu, and uses the underpinnings of such teachings to heal the broken kyber crystal in her lightsaber.
This is of note because it would seem that she actually taught herself how to do it somewhat from some related teachings but not teachings on how to do it specifically. We also see some "Lightsaber diagrams" in one of the books so it's likely there was a bit more information on how lightsabers worked in them even if not down to the detail of bonding a kyber crystal.
Click image to enlarge.
Lastly, I think it is worth noting that in The Rise of Skywalker we learn that Leia underwent Jedi training and even constructed her own lightsaber that Rey uses later on. Whilst we never see Leia teaching Rey on constructing a lightsaber, that I know of, she was training her. It's possible that as part of this training Leia also helped Rey with repairing the old Skywalker lightsaber.
