There is no "add list" or "add card" button. I've tried different browsers and computers and I still don't have this option. I also have admin permissions. Using a MAC, but I also tried it on a PC. The help guides says you can double click on any open space in the board to add a list, but nothing happens.
Are you a member of the board that you wish to collaborate on? It sounds that you are a member of the team that the board is part of but not a member of the board itself.
More information is available here: http://help.trello.com/article/717-adding-people-to-a-board
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