The House can be found on Home Island, and will always remain there. Complete the 'Investigate berries' and 'Collect more grass' quests to unlock it.
Upgrading the House will increase your energy limit. It can be upgraded 19 times throughout the game, with each upgrade requiring a different set of items.
For more info on upgrading the House, check the guides we have posted to our official Facebook group and Discord channel.
To learn more about building, check out the Crafting Stations section!