It's not required to get married when playing Mineral Town, but one of the game features includes marriage so you might as well go for it :) You can choose to marry 6 different girls; Ann, Elli, Goddess, Karen, Mary, or Popuri. Once you get married you can't cheat on your wife with one of the other girls. Don't think such bad thoughts! Before you can get married you have some requirements you have to meet.
House and Big Bed - No lady is going to want to live in that tiny little house you started out in. Before you can wed, you have to hire Gotz to upgrade your house twice. Also keep an eye on the TV Shopping channel on Saturdays. After you buy everything available and have your house as large as it can go, the Big Bed will be for sale for a price of 10,000 G.
Red Heart - When you talk to each girl (except for the Goddess) you can see how affectionate she is towards you by the color of the heart that appears on her portrait. When you first start the game all of the girls will be at a Black heart level because they don't know you very well! The more you talk to them, the better they get to know you. You can also give them gifts to help raise their love levels. Each girl likes different kinds of gifts and you can even gift-wrap them at Jeff's store before you give them out. A wrapped gift will give you better results then just giving the girl a gift with no pretty paper on it.
Buy the Blue Feather - When any girl you are courting reaches an Orange heart color, the Blue Feather will be for sale at Jeff's store. You can use the feather as a marriage proposal item when the girl you're after reaches the Red heart level. When you think she's ready, just equip the Blue Feather and press the B button. She'll accept your feather, visit your farmhouse, and then you two can wed 7 days later.
You MUST have an empty slot in your rucksack before you can buy the Blue Feather.
See all 4 Heart Events - You must activate her four heart events before she'll accept the Blue Feather. The heart events can trigger after you reached the black, purple, blue, and orange heart colors. The events also aren't restricted to happening only at that color; you can still see the black event even if her heart color is yellow.
Some girls will take more persuasion than others (*cough* Elli *cough*) so if she turns down your marriage proposal, just keep giving her gifts like normal. Then just try and give her the feather a week later. If she still doesn't want you, then just keep giving her items until she does. Be persistent!
Note: Persistence does not work well in real-life situations. Please do not stalk anyone and shower them with blue feathers. Thank you.
The Goddess is a whole 'nother can of worms when it comes to marriage. This lovely lady doesn't have a visible heart color for you to judge her affections with. She also has a lot more requirements you have to accomplish before she will even consider marrying you. Please check out her information page for all of the requirements necessary to marry her.
You aren't the only one trying for a girl's affection. You have rival bachelors in the village who are looking to get married too! Your rival for Ann is Cliff, Elli's is the Doctor, Karen's is that dorky Rick, Mary's is Gray, and Popuri's affection is battled for against Kai. The Goddess doesn't have any rivals for her affection, probably because she's such a high-maintenance girl! Each fellow has Rival Events that can trigger when a girl is at a Black, Blue, Green, or Orange heart color. If you see all 4 events, then the two of them will get married 7 days later. You'll only be invited to their wedding if you're in good relations with the bachelor.
Even if you're not invited to the wedding, you might accidentally stumble across it. If you know the date that the last Rival event occurred, go to the Church a week later and you'll be invited to attend the ceremony by Carter. If you tell him you have more farm work to do, you can escape from the cut-scene and talk to the wedding guests. When you're ready you can talk to Carter to reactivate the wedding, or just leave the Church.