It may be quite difficult to gather information regarding the history of a local ordinance. The process of passing an ordinance is much less complex than the process in the state legislature or Congress, and it usually creates very little documentation.
Locate the relevant sections on the topic in the current city or county code and look at the end of the sections for dates of passage.
Search news sources to determine specific dates of votes, e.g., "at yesterday's meeting the city council approved new restrictions on..."
The news reports may also provide some details regarding support or opposition to the measure.
Search for the meeting records of the local council or board. Often the minutes of local meetings provide very few details regarding what transpired in the meetings, e.g., "After a period of public comment, the council approved the ordinance by a vote of 5 to 2." Look for agenda packets distributed prior to a meeting, which may contain more details such as staff analyses than the minutes. Sometimes the local government process requires that a new ordinance be presented at one or more meetings prior to the meeting at which an actual vote is taken, so you may need to look at the minutes and agendas of one or two meetings prior to the meeting where the ordinance was approved.