Share Play is one of the new features that will be delivered this week with PlayStation 4 firmware update 2.00.
To assist you, Sony has released a brief tutorial video that takes you through the relatively simple Share Play process.
The option is accessed through the PS4's party menu and if you're the host, you'll see a fresh listing for Share Play. Then you select "Give Controller to Visitor," and this will hand control of the game to that visitor for up to an hour. Now, the host has to be a PlayStation Plus member but the guest does not; the guest doesn't have to own the game in question, either. Sony has dubbed this the "virtual couch" experience.
Update 2.00 also includes Themes support, a USB music player that enables custom soundtracks, YouTube sharing, and more.