What's the procedure a certificate authority (CA) must follow to get internationally recognized, like Verisign or GlobalSign?
To be intentionally recognized, the trusted certificate authorities (CAs) will need to get their root certificates pre-bundled with specific web browsers and operating systems (OS), like Microsoft Internet Explorer, Apple Safari, Mozilla Firefox, Google Chrome and Opera (et al.). The trusted root certificate list is usually updated periodically to add or remove certificates.
In addition, specific programs like Java or Adobe have their own trusted root CAs which is used in their applications (thanks paj28 for the reminder!). Adobe has a setting which allows all Windows root certificates to be trusted automatically. However, I think the process is not so straightforward in Java.
To be included in Microsoft's Root Certificate Program,
Similarly, Apple's Root Certificate Program requires root certificate authorities to meet certain criteria. This goes on for other browsers.
Other web browsers/OS may have their own specific requirements and legal agreements. Hence, to be as recognized as "internationally" as possible, a CA usually needs to contact all the major OS and web browser developers to obtain permission to be included in each pre-installed list of trusted root CA certificates.