It can 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
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.