I heard about an exclusive PS4 Beta. How does one sign up for that? I looked at the beta signup on the ESO site and did not see an option for PS4. Does anyone have any more info?

Read the bottom of http://www.tesoelite.com/2013/06/eso-on-the-play-station-4/ for beta signup options

The sign up should be for anyone, I don't think there is an option.

There is no available information for that at this point. You can discuss ESO on consoles in http://www.gamesas.com/topic/1462937-eso-coming-to-pc-mac-ps4-and-xbox-one/ And you can keep an eye on the Offical ESO site http://elderscrollsonline.com/en/