It might be difficult! Private companies are not required to make the same disclosures that public companies do. However, you may have some success using the following sources:
PrivCo - Provides business and financial research on non-publicly traded (private) corporations in the US and internationally
Mergent Online - Includes directory information from Dun & Bradstreet. Be sure to click the checkboxes for "D&B Private Company Database" and/or "D&B 20 Million Plus Private Company Search" to access this info.
Business Source Premier - Contains Datamonitor reports on private and public companies. Search by company name, and be sure to select "Company Report" as the Document Type.
Hoover's Reports via Nexis Uni - Search by company name.
For assistance researching a particular company, please contact the Judy Geczi.