It is much harder to find financial information on private companies than it is for public companies. While public companies are required by law to disclose detailed financial information to the SEC (available from the EDGAR database, Mergent, and Nexis Uni), private companies can decide how much information they wish to make available.
Both Mergent and Nexis Uni have information on private companies.
You can also find news articles about private companies by searching Business Source Complete, Nexis Uni, and Factiva.
Finally, be sure to check the company's website. Each company makes differing amounts of information available publicly, ranging from none to quite a bit. If any information is available, it may be behind small print links with titles like "financial information," "investor information" or "fact sheets."