Public companies issue stock and/or debt. Also, they are required to submit financial statements to a regulating authority. Private companies are not required to do so.
Read a company's financial statements and annual reports which can be found on the company's website or the SEC's EDGAR database.
Read news articles, analyst reports and other secondary sources to round out a profile.
To find private company information, in addition to looking at the company's website, check the following Fordham Library databases: ABI/Inform, Hoover's, Business Source Complete, LexisNexis and ThomsonONE Investext.