Note that, unlike our Virtual Families games, there is no marriage (or dating) in Virtual Town. You adopt only one child in Virtual Town in order to have a successor. It is not possible to adopt more than one child at a time.
The child will age along with your mayor. When your current mayor reaches the age of 60, he or she will retire to The Island, and the game will ask you to make the child the new mayor. If the child is under 18, they will automatically start their new life as the mayor at age 18.
If you'd like to know how old your mayor is, this article will help you.
You can adopt a child when the Adoption Lady visits your town, which usually happens every few days. You can find her in the town square in front of Town Hall, when she is in town. She will bring several children with her when she visits, and she will tell you about them when you tap on her. To see all of the children, scroll through their details as you did when you were choosing a mayor at the beginning of the game. If you see a child you'd like to adopt, tap the Adopt button. If you want to see the other children, tap Try Again. You may continue looking through each of the children as many times as you like.
If you don't want to adopt any of them, tap the red "X" in the upper right corner of the Adoption screen to close it. You can then go about other things in your town. The Adoption Lady will remain in your town until the end of the day. She will return in a few days with other children for you to see. If you accidentally close the window or want to look at the children again, tap the Adoption Lady to go back to the Adoption screen.
If you have played the game for more than a few days, and you want to call the Adoption Lady, you can pay a fee to have her visit your town the next day. To do that, enter Town Hall and sit at the mayor's desk, then tap on the Adoption icon. If you don't see the Adoption icon, you haven't played the game long enough to enable that option and will need to wait for the Adoption Lady's next visit to see more children.