I do a lot of non-work AI stuff on my own, from pair programming with AI, asking it to generate whole things, to just asking it to clarify a general approach to a problem.

FWIW, in a work environment (and I have not been given the go-ahead to start this at my work) I would start by supplementing my codebase. Add a new feature via AI coding, or maybe reworking some existing function. Start small.