After speaking with Uniegost, your next task is to build a simple house. This is a core mechanic of the game. First, you'll need to gather resources. You'll need approximately 10 Logs and 10 Sticks for the foundation and frame, and then more for the walls and roof. Equip your Stone Axe (craft one if you haven't already: 1 Stone, 1 Stick in crafting menu 'C') and chop down some trees. Use your bare hands to collect sticks from the ground. Once you have enough, open the building menu (Q), navigate to 'Buildings' -> 'Houses', and select 'Small Simple House'. Place the blueprint in a suitable location (ensure it's not too close to other settlements). Once the blueprint is placed, you'll see the required materials for each section. Use your axe to 'build' the foundation, walls, and roof by holding down the left mouse button while looking at the highlighted sections. Completing the house will advance the quest.
