Before you can have a child (and you only get one) you'll need to be married. One or two seasons after the wedding ceramony you will wake up one morning and feel ill. Your husband will notice and take you to the Clinic. At the Clinic the Doctor and Elli will inform you that you are pregnant. The two of you will be happy and you'll return to your farm.
While you are pregnant the farm will still need to be maintained. You don't take any time off for bedrest and your husband still won't help you with any of the chores. Hmph! The game will continue on as normal for another 2 seasons.
After 60 days you'll finally give birth. Elli will come by to help you with the delivery of your new baby daughter. Everyone will be happy and you get to select her name. The next day you'll be up and doing chores like normal, while your girl stays in the bed all day. Don't worry, she'll be fine laying there by herself. The baby doesn't require any maintenance like your animals do.
Since your little kid is in bed all day there's no way to give her gifts.
Once another 60 days has gone by, your husband will wake you up in the morning. He will be in a panic because your child seems to have fallen out of bed! You can choose to stay home, or take her to the Clinic (option 2). When you arrive Doctor says that she's fine. When the three of you return back to the house your baby can now crawl around.
Now that she's out of bed you can give her gifts. The baby likes all sorts of sweets like Ice Cream, Cake, Hot Cakes, Honey, Cheese Cake, and Strawberry Milk. So you don't rot out your child's teeth (even though she doesn't have any) you can also give her Hot Milk, Wild Grapes, and balls of Yarn to play with.
At the end of another 60 day period, your husband will excitedly bring something to your attention in the morning. It turns out that your baby has finally begun to walk! Your baby will like to receive more gifts such as Apple Pie, Chocolate, flowers, and Omelette Rice.
Once the baby begins to walk she has completely "grown up" and won't age anymore. She will never leave the inside of the farm house and she won't help you with any of your farm work.