Proposed Canon
The process is unclear; casters captured in battle, especially after a side is destroyed and they become barbarians, sometimes join their captors, particularly as an alternative to croaking. A unit can apparently turn in the field if properly motivated; of course, Obedience, Loyalty, and Duty all work against this process.
When Jillian was under the influence of Wanda, and would not attack the wounded dwagons, Jaclyn tried to prod her into choosing some course of action, including abandoning the fight or turning to Stanley's side and joining up with the dwagons.
Later, Jillian asked Wanda to turn and join the Royal Crown Coalition.
Vanna, a turnamancer working for Faq on contract, successfully turned Jitterati Warlord Duncan Scone to Faq, after Faq had sacked two of his side's cities and staged side-wide betrayal by their natural allies. The indication is that a turnamancer has magic that can assist in the speed and success of turning. She could not instantly turn a Decrypted Ansom at a distance, however. It remains to be seen what that means.
It is also apparently possible for a unit to Turn with the permission of their Ruler, presumably as part of a trade or surrender agreement (or occasionally for more bizzare purposes). This action is twice demonstrated in the story "Inner Peace through Superior Firepower", and apparently uses the formal oath “On orders from my Ruler and with my full personal consent, I hereby pledge allegiance to the side of X, and its Ruler, for all the rest of my turns”. What oath, if any, is spoken to seal an unordered Turning is unknown.
In Digdoug Episode 9, we see a Barbarian caster joining a side for the first time. This is referred to as "aligning" and is apparently distinct from regular Turning.