Companies often describe the competitive environment and list their top competitors in their 10-K report to the SEC. Read "Item 1. Business" or search the text of the report for the words competition or competitor.
Many databases offer profiles of public companies that include lists of the company's top competitors. Using one of these profiles is an easy way to find the companies that are active in a particular industry.
If you want to build your own list of competitors based on variables like location or number of employees, use one of these databases: