My method

Whenever I talk to people who are apathetic to politics I always say "apathy is a political statement." I've found it to be pretty effective once I explain what I mean.

Apathy is a privileged view of the world. This is a somewhat extreme example, but if you are apathetic to politics while there are people living on the streets you are essentially saying "those people's lives don't matter. I don't care if they die, are harmed by police, etc."

This is how I converted my girlfriend actually. Good luck out there comrades. <3