About 20 days after getting married, the female-side of partnership (the player's wife or the female player) will begin to feel ill. At the Clinic, Alex will let you know that the two are expecting a baby.
The pregnancy lasts for 2 seasons. When the time is right the two of us will end up back at the Clinic, where you'll wait a bit for the child to be born. At the Clinic, Woody will also appear and give the three of us a new Baby Crib. The crib can be placed anywhere in your house like any other piece of furniture.
The child will stay in the crib for a while, but you can pick them up by pressing the A Button. Inside Villagers summary menu you'll find a heart meter for the child. If you want to make the baby happy you have to pick it up everyday, and play with it using the Rattle and Picture Book you can buy from the Junk Shop. You can also feed the baby meals like Milk.
When the baby cries it makes a horrible, screeching noise so try and comfort it as quickly as possible!
Eventually after about 2 more seasons the child will grow to a second stage. After a visit to the Clinic they will be able to walk around, and will be out of there crib when you wake up in the morning. You can still put it in the crib if you want to force the baby to take a nap, and they will quietly sleep there until you leave the house. When you come back inside they'll be back sitting at the foot of your bed again.
You can even abuse the child by dumping them outside, but it always seems to find its way back home.
Once the baby has grown to the toddling stage it won't mature anymore and stays at that stage forever. The player is not prompted to give it a name and the child's gender has never been revealed. This is very similar to Mineral Town games.