Unlike public companies, private companies aren't required to disclose financials and other info--so it can be difficult to find detailed info on private companies. It's even more difficult if it's a small private company.
Beware: It is difficult to find high quality info on private companies. Even though the sources listed here are "better than average quality," sales figures and other private company info are often wrong even in these sources.
Large Private Companies
Try Hoover's and Business & Company Resource Center. There may also be many articles in business periodicals. If the company competes with public companies, they could also be mentioned in the public companies' SEC filings. Well-known private companies may be found in the International Directory of Company Histories or books on the company may be found in the library catalog.
Medium-Sized Private Companies
Try looking for articles in ABI/INFORM. If you can't find articles in ABI/INFORM, you may have more luck in Factiva which includes local newspapers and many industry periodicals.
If it's a Michigan company, also try the Michigan specific sources listed under the Michigan Companies tab.
For retail companies that compete locally, you may be able to use free web "yellow page" directories to identify competitors.
Consulting Firms can be particularly difficult to research. The print Consultants and Consulting Organizations Directory at the EMU Library may often be the only source of info you can find.