Go into the crafting menu (default Q) and go into the "Structures" subsection. Build some foundations first and add walls, doorways, doors and ceilings to make it your home. You need wood to build a base.

Bases can be upgraded to stronger materials. Wooden walls can be upgraded to stone walls and wooden doors can be upgraded to metal doors. Stone and metal structures cannot be damaged by tools but can still be damaged by C4. To upgrade your base you need a repair hammer - which can be crafted from 1 stone and 1 wood. Once you have the repair hammer equipped, hit the wall to bring up the menu and select "upgrade." Make sure you have the required materials in your inventory to upgrade. Walls and doors need to be at 100% health before they can be upgraded.

Your base can be damaged by other players but can also be repaired. To repair your base, equip the repair hammer, hit the damaged wall and select "repair" from the menu. Make sure you have the required materials in your inventory to repair.

Workbenches are used to protect your base.