If an RP is public, than that means you are free to post in it like you would any thread on the forum.
If the RP is private, however, you simply have to PM the RP's owner and ask what are the qualifications required to participate. After that, it's just a matter of fulfilling those qualifications and being allowed to post. Not however, that some Private RPs are only open to specific people, so you won't be able to join them even if you asked.