One of the easiest ways to see democracy in action is to attend a town meeting.
You can probably find your town’s next meeting online, and there’s a chance the meeting will be livestreamed. That way you can take a look and see if you want to attend the next one in person.
In some places, the city hall meetings are large, but there are smaller community board meetings. In my case, I looked up the next community board meeting, and I’ll go to that in person — it’s not livestreamed.
It took me about 12 minutes to find the information I needed – it should take you about the same.