There are a couple of ways. As with every play, if you're seeing a production of it, the audience has to accept that this really isn't Oedipus, those lights aren't really the son, the costumes usually aren't made of authentic material, etc, etc. The audience needs to suspend the disbelief, otherwise the play won't be very enjoyable.

When simply reading Oedipus Rex, the reader has to believe that Oedipus never mentioned to Jocasta that he had been abandoned and raised by shepherd, that he killed a man on the way to the kingdom, that he feet had been bound together (or that she had never seen the injuries on his heels.) Readers also need to believe that Jocasta never told him that she had a child that was destined to curse the kingdom that she abandoned in the wilderness. Also, if one of them did tell their story to the other, there was some reason the listener didn't chime in with, "Hey, that kinda sound like something that happened in my life!"

The reader also needs to believe that Oedipus wouldn't have recognized the king (either as the king or as his father) or hadn't seen any resemblance of himself in Jocasta. Also, no one else in kingdom ever mentioned the story of the abandoned child or a family resemblance to Oedipus.