Skyrim Hearthfire is the second official expansion (DLC) for the game The Elder Scrolls V: Skyrim. (The first official expansion was Dawnguard)
Hearthfire was released by Bethesda on September 4, 2012, exclusively for the Xbox 360 (for $5/400 Microsoft points), and is scheduled to be released for the PC and PS3 at a later date.
How to build a house in Hearthfire
Purchase land by obtaining a Deed. Locations include The Pale, Falkreath, and Hjaalmarch.
Design house using Drafting Table and Carpenter's Workbench
Gather Building Materials
How to adopt a child in Hearthfire
You will receive a courier letter from Constance Michel asking you to come to the Honorhall Orphanage in Riften to adopt a child.
You need a house with a child's bed and small dresser so that your kid can move in. It can be a new house you build, or an improvement to an existing house in one of your cities, such as Breezehome in Whiterun
Not all children can be adopted. See here for a complete list of adoptable kids: List of Adoptable Children in Skyrim Hearthfire
Talk to Orphan and offer to adopt him/her.
Once adopted, the children can bring pets into the house. See: Skyrim Hearthfire: Pets
The Beginner's Guide to Homesteading
How to start the Hearthfire DLC for Skyrim