Go to the in game store at the main menu. Thats where you will access your season pass items. However they haven't released any of the skins pack or other DLC that is included in the season pass. They'll be doing that over the course of a few months.
The "new story campaign" has not been released as of yet, nor has their been any official word of a "DLC Schedule". What's disappointed me about the 'Season Pass' is that most of the skins are unlockable in-game, I was excited when the 'Millenium Skins'
Pack showed up last week, but found that I'd unlocked most of them in-game all ready. I feel bad for those who went out and purchased the Deathstroke, Joker or Batman Avatar Costumes before launch to find that those are all unlocked from progressing through
the story as well. The 'Initiation' DLC will likely show up first before the "new story campaign" does for they've all ready released some details on this particular download...:-)