The online costumes are released Once a week Beginning July 1st and every 7 days afterwards... Once the DLC is downloaded you have to find the proper "Spider" logo hidden somewhere in the city and then must take a picture of said logo before you can use the suit - so you cannot find these suits until after you beat Chapter 3 and earn the camera.
But for ease here's the dates:
07-01-12 Scarlet Spider (2012) Suit - the image you have to photograph is on a brick wall near a bridge inside Central Park
07-08-12 Black Costume from Spiderman 3 - This one was kind of a pain to find. In the city there is a small park just to the north of the Daily Bugle, on the south side of this park is a Gazeebo - go inside and look directly up. Now the problem is that it is dark in the gazeebo and the spider icon is black, so I didn't see it the first few times I looked. Eventually I DID see it - now I cannot unsee it of course - just took the picture and viola Classic Black Suit.
07-15-12 Future Foundation Black Suit (in the comics, Spidey has joined the Fantastic Four, who changed their name to the Future Foundation - this is one of the new suits he wears while with that team).
07-22-12 Big Time Suit (Worn during the "Big Tim" story arc in the comics (2012))
07-29-12 Negative Zone Suit (Spiderman dons this silver and black suit whenever he enters the Negative Zone)
Remember - once you have these costumes unlocked you DO have to go back to your apartment in order to switch between them. And they have no value outside of cosmetic - meaning you'll look different, but you won't unlock any special abilities or talents. Have fun!
There is also a "special" August suit to celebrate Spiderman's 5oth Birthday. Its basically the regular suit from the game, but Spiderman will also be sporting a "Birthday Party Hat" that has some 50th anniversary logos on it. As far as I know this suit doesn't need to be found.