Researching your City's Government Structure
The municipal code should help you understand your municipality's structure. Look for sections of the code which define powers of the city council, mayor, etc. The resources below will help you locate the municipal code as well as state's statutes.
Finding Recently Passed or Adopted Ordinances
Although the links above will allow you a city's ordinances in their codified form they do not arrange them in the order they were passed or adopted. You will have to go to city's website. You can Google the city's name and the phrase "adopted ordinances" (e.g. Chicago and passed ordinances) or just name of the city and the phrase "city government." In either case, you are looking for the output of the city council or some committee.
Some cities use a service called Legistar to keep track of meetings. These sites will have "legistar" in the web address so a search for your city's name and "legistar" may return their legistar cite, if they have one. If you find one, you may be able to find ordinances by clicking on the "legislation" tab and selecting ordinances. Usually you can click on the search legislation button without entering a search term, that should bring up all the ordinances that are in the system.
See the links below for examples. Not all cities who use Legistar have a legislation tab.
Newspaper articles may discuss recently adopted or passed city ordinances as well as tell a little about the city's history and issues. Use the sources below to search for newspaper articles.