Professor Farnsworth introduces his new crew, Fry, Leela and Bender, to the other Planet Express employees - Hermes Conrad, the bureaucrat; Amy Wong, the Chinese intern whose super-rich parents own half of Mars; and Dr Zoidberg, the staff doctor who knows nothing about humans.
Afterwards the crew go on their first delivery, with Amy accompanying them. It's only to the Moon, nothing special, but to Fry this is a dream come true. They get to the moon and Fry discovers that there is an amusement park on the moon. The delivery is a crate of stuffed toys for one of the amusement games, and once that is delivered the crew explores Luna Park.
Amy discovers she accidentally left the keys to the ship with the crate, so they are now in the claw game. She tries to get them back before Leela (who has been appointed captain of the ship) finds out, but she is not very good as the claw keep dropping the keys. Bender tries putting his arm through the game to grab the keys but gets caught and is thrown out of the park.
Fry gets bored of the park and wants to explore "the real Moon", and find the site of the first lunar landing which has been lost for centuries. He and Leela hijack a cart and go exploring, but soon their oxygen runs out and they have to go to a Moon farmer to get some more. He only lets them have some if they do some chores for him. Whilst doing the chores Fry and Leela discover Bender has been trying to romance the farmer's 3 robot daughters, and the angry farmer chases Bender off with a shotgun.
Fry and Leela, now with oxygen, manage to escape and find the lunar lander, where Leela tells Fry off for getting them into this situation. All because he wanted to see the Moon. Fry apologizes and says it was his dream. Leela looks out of the lander window and sees the Earth from space, and realizes what Fry meant, and forgives him. Amy then picks up the lander with a magnet attached to the Planet Express ship (she got the keys back by picking up everything in the game!) and they all fly back to Earth.