A powerful tool for understanding and comparing stocks is the use of financial ratios. Many of the websites and databases will provide financial ratios on companies.
Financial ratios are very useful, but they can be confusing at first. This link from the Small Business Administration, is a good introduction.
When researching any company, the first question you need to answer is: Is the company public, or private?
If the company is public, that means it is listed on a public stock exchange. If a company wants to be on an American stock exchange, they need to publish a lot of information about themselves, in a strict format, to the United States Securities and Exchange Commission (SEC), an independent agency of the United States Government.
The SEC search engine is called EDGAR, and you can search using company names or stock ticker symbols.
The most sought after documents on EDGAR are usually the 10-K reports, which each public company has to file annually. 10-K's are submitted in a strict template for all companies. The SEC provides a very helpful guide on How to Read a 10-K / 10-Q as well. Sometimes 10-K's make reference to additional information being available in other documents, such as 10-Q's and Proxy Statements. These documents can be found on EDGAR as well.