Preaching is one of the responsibilities of a peteran priest. It provides XP and some simoles. I believe that it will also give a positive focus buff. All of this is good but how does one maximize the benefits from preaching?
Popularity affects the offering but what affects popularity?
One of the first Guides Carl wrote was the Peteran Guide and I believe his target date for putting new Guide articles up is Sunday. In the meantime, what I can tell you to do is to listen carefully to congregation reaction. Select a given sermon tone and if you're hearing cheers or laughter, then that's good. If you hear boos, then try and switch the tone.
The other tip I can provide is go on a conversion spree — walk around the Kingdom and convert lots of peasants to the Peteran religion. That shoots up popularity a great deal — more than sermons.
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Edit: Lol. The head Peteran Priest steps in to make a sermon.