Each certifying organization is different and will have different procedures. But basically the process will go something like this:
A packaging manufacturer decides on a certification it would like to obtain
The manufacturer will then purchase the certifying organization’s standards requirements and study them
The manufacturer will compare the standards and procedures it uses with the ones the organization requires
The manufacturer may hire a consultant to aide in implementing the standards and procedures if they feel they need help
If the manufacturer believes they are in compliance, they will pay for a registered third party to audit their facility
After the audit, they will address any non-compliance issues, and once those are taken care of, the packaging manufacturer will acquire their certification.
Usually these certifications need to be renewed (reviewed and paid for) every year or every several years.