Just to clarify, the game only has local multiplayer/splitscreen. No online/LAN multiplayer.
At the moment, you will need a controller for each player. I think if you mix desktop and controllers, there's issues... Anyway, In the party/player setup screen, pressing start or an action button on a controller should open up a new panel. If this doesn't happen, it might be the type of controller you're using. Xbox 360 controllers have been tested and should work natively on Windows.
If you're still having issues, let us know.