Your ship has crashed and you are rescued onto a ship full of girls!
You are out in galaxy, and are trying to get with the galaxy angel.
The girl will tell you what you need to complete the mission, but it usually involves going somewhere -- usually a planet or the archive -- and finding something to bring back.
Another way to increase a girl's points is with gifts.
Mint likes the chicken Cosplay item, Ranpha really likes the rings, Forte prefers guns, Milfeulle likes to cook with frying pans, and Vanilla likes vodka. One is in the lamp in your room, another in the center windmill of the holodeck; the red ball in Vanilla's room and the right eye of Milfeulle's room both have secrets, as does the mug in the kitchen.