Hearthfire is an expansion for The Elder Scrolls V: Skyrim, enabling players to adopt children, build homes, structures, and other items from the ground up. You can only start the Hearthfire DLC after conversing with the Jarl in Morthal, Dawnstar, and Falkreath, and completing the tasks assigned.
Steps

Activate the Hearthfire expansion. A letter will be sent to confirm that a plot of land is available for purchase.

Travel to the Jarl's castles in Dawnstar, Falkreath, or Morthal. These cities are home to the Jarl, from whom you will purchase the land.

Talk to the Jarl. The Jarl will assign you a task to complete in order to be eligible to purchase land.

Complete the Jarl's request. The tasks will vary depending on the city you visit. For example, if you speak with the Jarl of Falkreath, you will be instructed to kill the bandit leader at Bilegulch Mine.

Return to the Jarl after completing the task. The Jarl will grant you the title of Thane (a noble rank), and you will be allowed to purchase land within the Jarl's jurisdiction.

Ask the Jarl about purchasing land. The Jarl will have the steward speak with you to finalize the transaction.

Confirm with the steward that you wish to buy a plot of land. The cost for purchasing land is 5000 gold pieces.

Choose to purchase the land. The steward will provide you with a deed to your plot of land.

Use the map to navigate to the plot of land you just purchased from the Jarl. Once you arrive, a set of tools and instructions will appear. You can now begin building your house and adopt children as per the Hearthfire expansion.
Tips
- Consider appointing your steward as a Housecarl after purchasing land from the Jarl. This will allow you to buy wood, stone, and clay directly from the Housecarl.