There are many ways to serve a community: voting, working, volunteering, learning, parenting, etc.
If your public service-bliss is to geek out on government operations, there is nothing more basic than understanding the budgeting process.
Understanding how laws are made and how political parties operate are equally important, but if you don’t know how “public” money is raised, allocated, and spent, you will always feel out of the loop.
Many local governments have budget committees that include citizen participants, but there is also this: Participatory Budgeting:
Generally: Wikipedia Participatory Budgeting