What special knowledge was John taught as a priest's son in By the Waters of Babylon?

John learned basic first aid.  He tells readers in paragraph five that he was taught how to stop a person from bleeding out.  

l was taught how to stop the running of blood from a wound and many secrets.

A second skill that John learned was how to read and write.  As a priest, he needs to know how to do both, because he has access to books left over from the great burning.  His ability to read will help John transform his society and bring back some of the lost knowledge.  At the end of the story, he vows to return to the city and begin educating his people.  

Nevertheless, we make a beginning. it is not for the metal alone we go to the Dead Places now— there are the books and the writings. They are hard to learn. And the magic tools are broken—but we can look at them and wonder.

Lastly, as the son of a priest, John was taught the ways of the dead houses.  This means that he was allowed to go into the homes located in the Dead Places.  He studied their layout and the remains of the people in those houses, but John doesn't elaborate on any specifics of what he learned from those houses.