Some great advice for starting out in local politics from Berkeley political science PhD student Rachel Bernhard:
Consider joining a commission or the local branch of your party (Democratic, Republican, whatever). Pick a commission if you feel more urgency about tackling policy issues in your area, and pick a party if you feel more urgency about changing what issues your party is focused on or how it connects with people.
A board or commission–in most places they’re the same thing–usually meet on some intermittent schedule (like an evening once a month) that focuses on one policy area: police oversight, economic development, the status of women, schools, etc. You get to hear what’s going on in your city from the people working on those things (e.g., the police chief), and on the basis of what you hear, make recommendations about what should be done. Most cities and states post vacancies on their websites, so start there.
Your party may have a local club or a county committee; how parties are structured varies a lot by state. Parties decide who to endorse in local races, help raise money for those candidates, and establish platforms (what issues they’re going to prioritize in your area, and sometimes how they think it would be best to solve them). They also tend to have regular meetings, and often host educational events with speakers too.
If you wanted to, you could certainly do both, but I’d suggest starting with one and seeing how it fits in your schedule. Prioritize long-term sustainability of commitment when you are giving up your time: change is made by those who show up regularly.
This is unsexy stuff. There’s no Barack Obama (yet…stay tuned), no protesting in the streets, no Spanish-language posters calling Donald Trump a pendejo in the bathroom. That’s why it’s so important that you, average lady or gentleman or gender non-binary that you are, show up. You have an important voice and perspective: I know this because I see it in my newsfeed every day. If we want our politics to change–not just our president to change, but the day-to-day governance of our people–so that something like what we are facing now can never happen again, we have to roll up our shirtsleeves and get into the dirt together.