There are 6 girls that you can marry. Each girl has a colored heart that appears on her chest, letting you know how they feel about you. The only exception is the Goddess, who has an invisible heart. The heart colors will change depending on how you treat each girl. The colors will change starting with black, purple, blue, green, yellow, orange, and then finally red. When she gets a red heart you can buy a Blue Feather from Jeff's shop and ask her to marry you. There are also events that will occur, called "heart events", when you've pampered each girl up to a specific heart color. If you choose your birthday to be the same as one of the girls', her birthdate will change to an alternate date.
You can't marry the rest of the villagers, but being nice to them is still preferred. When you're nice to the residents they'll in turn be nice to you. Some of the villagers will even give you cooking recipes if you've been nice enough to them. Giving them their favorite foods is always a plus.
The potential wives aren't just yours alone to court. You will have to fight for her affections with another man in the village! They have their own series of Heart Events that occur with the girls and when you see the 4th one, they'll be married a week later. If you're good enough friends with the bachelor, then he'll invite you to the wedding. Even if you're not invited, there's a chance that you can accidentally stumble in on the ceremony at the Church (which I've done at Popuri and Kai's wedding).
Note: I've noticed in the English version that the Rival's blue heart events can happen even if the girl isn't at the blue-heart level. Be careful!
When you connect Friends of Mineral Town to the Gamecube edition of A Wonderful Life, these two folks will come and visit your town. You'll be able to buy special items from Van and Lu will give you some nifty cooking recipes that the villagers of Mineral Town won't know.