How to increase authority points?

[PBI]

You are correct that Authority affects loyalty; with high Authority generals pretty much never desert no matter how disloyal, but if it's below about 4 crowns putting an army in charge of a general with less than 4 loyalty or so is a definite liability, and risking leaving a captain in charge is pretty much as good as throwing your troops away.

I find two methods effective in raising authority:
1) Making sure your king is also a great conqueror; a lot of the traits picked up by good generals boost authority, such as the "Conquering Hero" type ones. It's a good idea to get started on this with your heir before he takes the crown, he'll still get the authority-boosting traits even though he won't get any benefit from them until he becomes king.
2) Using a lot of assassins and spies; so long as you don't mind your king being a high-Dread general this is a very effective way of boosting authority, especially if your King isn't likely to be much good as a general. Most of the "master of assassins" type traits and ancilliaries give big authority boosts, I suppose because all your generals will be too terrified to risk acts of disloyalty. This one is only good for the current king, though, you can't groom a weak faction heir to be more authoritative this way.

Unfortunately there is no way to choose the faction heir directly, which is doubly annoying since it seems to be selected more or less at random if the current king lacks sons; it quite often goes to someone completely useless in place of much better candidates. The best you can do if you get someone truly hopeless is to deliberately get them killed in battle and hope the replacement isn't even worse; if he's just a mediocre though it's definitely good to groom him to rule by sending him on a conquering spree (faction heirs make ideal Crusade leaders); I very much take the sink or swim approach, either the heir will become a great general and prove himself worthy to rule or he will die trying.