PubMed Central accepts author manuscripts (the version of the article that has been through the peer-review process but has not yet had editorial changes made by the publishers) of papers published in journals that permit self-archiving.
There are two submission systems, one for NIH-funded and one for UK-funded research. In either system, someone with access to the author manuscripts submits the file(s), then the principal investigator (PI) has to sign in and confirm the submission.
There are FAQs and illustrated help pages linked from the front page of each system.