First, you need the second house upgrade which adds a crib and 2 toddler beds. Second, you need to reach 8 hearts with a candidate (Alex, Elliot, Shane, Harvey, Sam, Sebastian, Abigail, Penny, Haley, Emily, Leah and Maru). You'll have to go buy flowers from Pierre. Once you're dating, keep increasing the hearts until you reach 10. Then, on a rainy day, go to Tide Pools on the beach (past the plank bridge). There you will see an NPC (Old Marine) who will sell you the Mermaid's Pendant for 5000 coins. Give it to the NPC you want to marry, who should have 10 hearts. Wait 3 days and voila, you are married! Now we just have to wait; Every night there is a chance that your partner will ask you if you want to have a child. Answer yes and wait for him to be born or adopted.