Five of the game's bachelors have visible hearts that appear on their portraits when you converse with them. The heart color lets you know their current feelings towards you.
Before you can marry your guy, you have to go through a series of Heart Events. Each event will trigger after you've raised his heart color to the proper level. You have to see all 4 of them before he'll marry you. The events will activate once you've raised his heart color to Black, Purple, Blue, and Yellow.
Besides seeing all 4 heart events, you also have to of upgraded your house to its largest size and have purchased the Big Bed. The last think you'll need is the Blue Feather. It will appear in Jeff's Shop inventory once you have made one of the boys' heart orange-colored.
When the boy has a red colored heart on his portrait, hand him the Blue Feather you bought. He'll accept your proposal if you've met all the requirements. If he declines, make sure you've seen all of the Heart events. Sometimes a boy just need a few more gifts before he'll change his mind. The two of you will get married a week later and the ceramony will take the entire day. The wedding can not occur on the same day as a Yearly Event so it will automatically be postponed to the following day.
Won, Kappa, and Gourmet have invisible hearts. You still have to give them gifts in order to woo them, but you can't tell how far along you are in the love process. Those three secret bachelors have a different series of events that must take place before they'll accept your Blue Feather.