Do you have an e-ticket with a bar code? If so, you go to the entrance (as if you already have a ticket in-hand), not the ticket booth. They will scan your e-ticket, take your picture, and give you tickets. It literally takes less than a minute.
I should add that we went to the DCA entrance from the Grand Californian to activate our tickets and they did not even ask to see passports. I had them in hand, asked if they needed to see them, and they waived us through without looking at them. I would make sure you have them with you just in case though.