How does the person doing the reading know to say ‘letter from Paul’ when in the prayer book it just says Corinthians etc.? I’d like to do the readings but I don’t know these details.
Lectors who are doing the readings from the Bible at mass read them from a book called the lectionary. The lectionary is formatted to show the lectors which Bible passages to proclaim in which order on which day. Printed above each reading is the preface, for example, “A letter from Paul to the Corinthians.” After the Bible passage the lectionary prints a conclusion such as “The Word of the Lord” or “The Gospel of the Lord.”
If you are interested in doing the readings at mass, simply approach the priest or any of the ministers whom you have seen doing readings and let them know you are interested. (They will probably be thrilled to add a new voice to their ministry!)
Someone will arrange for you to have a brief training/orientation session to make sure you understand the procedures for the lectors at that particular church. Always before it is your turn to read someone will insure you know which passage you are to read and where to find it in the lectionary.