To recieve Bethesda's anti-patches you'll have to be connected to the internet when you launch the game. The game will automatically look for the lastest game updated or patch, before it starts up. It will tell you "A new update has been found" and you'll have the option to "X update or O cancel." You don't use the PSN store for patches, and you don't need to be signed into your PSN account, just an internet connection that is active and running, it can either be a wired or wireless connection it's up to you. Just remember one thing, if your PS3 doesn't have an internet connection, or you don't have access to a connection you can use, then you will not be able to receive any patches from any games.
My sugggestion however is not to even bother with the steaming pile of garbage that is Skyrim and Bethesda Softworks. There are WAAAAY better games out there other than Skyrim, and the PS3 version of Skyrim is AWFUL. You'll have nothing but headaches from the game, nothing but constant crashing, constant frame rate dips/sluggish performance. You'll always have to have a computer connected to the internet right beside you using UESP.net(Unofficial Elder Scrolls Pages) to look at every single quest because every single quest in the game can break in the blink of an eye, and you won't be able to complete them.
If this is your first time playing an Elder Scrolls game, and you're interested in others get the previous game Elder Scrolls 4: Oblivion. It's quite graphically dated now, but it actually runs the way it is suppose to, thanks to the awesome competent work of 4J Studios. You can find the Greatest Hits version for dirt cheap online. Don't buy the Game of The Year edition of Oblivion, despite it having all of the DLC that Bethesda allowed the PS3 to have. There are far more bugs in the GOTY version that in the non-GOTY editions.
Like what was said above Skyrim has more glitches on the PS3 version and because of that the DLC Dawnguard may never come out for PS3. Skyrim still is an amazing game even with the glitches (to me it seems a lot less than what people complain about). In the game menu (maybe when you press start in game) look for the number 1.7 because that is the newest version of he game.