Sony's PlayStation E3 2013 press conference will be held on June 10, 2013 at 6 p.m. PT. Invitations were sent out today, confirming the date and time. The press conference will take place following Microsoft's Xbox press conference, which is scheduled for 10 a.m. PT, as well as Electronic Arts and Ubisoft the same day.
Nintendo will have a booth at E3, but will not hold its own press conference this year, as the company is opting for smaller, more controlled announcements through their Nintendo Directs. Odds are they will have one the day before E3, as they did last year.
As for what Sony is planning for their presser, it's reasonable to assume that it will focus primarily on the PlayStation 4 and PS Vita, as the PS3 is on its way out; that said, you can still expect them to showcase games like The Last of Us, Beyond Two Souls, Rain, Tearaway and Killzone Mercenary.
As for the PS4, we already have had Killzone: Shadow Fall, Knack and inFamous: Second Son announced for the console since February. I'd bet that we finally get to see the console, get a firm release date, a price on the console and even more games.