The readings at Mass are rarely sung. It's a pity because singing the readings lends and incredible dignity to the text (and the English in the OF needs that!).
Well, perhaps it is time to think about this. Truly, it is a marvelous thing to hear. But how is it done? The old Liber Usualis contains 14 pages that are a model of clarity. These pages explain the tones and how they work for each reading (Prophecy, Epistle, Gospel) and provide various choices. The explanation is as lucid as I've seen. There is a bit of a learning curve, but with this guide, it does seem that anyone who can manage to navigate a few pitches could do it.
Here is the excerpt from LU, which will be used at the Celebrant Seminar in a few weeks.