In the Hearthfire DLC for Skyrim on the Xbox 360, one of the new features is that you can adopt a child to live with you in your new house.
In order to adopt a child, you first need to purchase a plot of land and begin to build a new house on it. Furnish it enough to have an extra bed for your new child to sleep in.
Once that’s done, head over to Riften and look for the Honorhall Orphanage. Speak with Constance Michel and ask to adopt a child. She will be thrilled!
All you need to do after that is to speak to one of the children and ask to adopt them. Once they accept, fast travel back to your home and you should find them there.
Check out my other guides if you need help building your new house, or if you need to figure out how to assign a steward to help build and furnish your house.