Thanks for your question. Corporate ownership is very hard to unravel. Some companies make it very clear through their annual report or website who they own. Some don't.

First step is to see if the company that interests you is at all up front about ownership information. You might check if any of the companies have a website which give information about ownership or have an annual report available. You can access corporate annual reports as well as other types of corporate records which must be filed with the SEC using their free EDGAR service, http://www.sec.gov/edgar/searchedgar/webusers.htm.

The easiest way I know of to determine corporate ownership is to find a library with a subscription to Corporate Affiliations, a database of accurate who-owns-whom information.
The online version covers public and private companies. The print version has separate volumes for each. Many libraries subscribe to this resource, and if your local library or university library doesn't, they can access the information for you through interlibrary loan.

As a last resort you might try contacting the company directly, your questions might get a frosty reply or the enthusiasm of a company looking for new investors. You might also try contacting industry peers or competitors. However information obtained this way is not very reliable.

Keep in mind that private companies aren't required by law to disclose as much information as public companies. They will be harder to find information for.

If anyone has other suggestions, please add a comment.