Building a base requires a substantial amount of raw materials. The two primary resources are wood and stone. To gather 'Wood Logs', you'll need an 'Axe' (Hatchet, Fire Axe, etc.). Find large trees in forested areas and chop them down. Each tree yields multiple logs. Be aware that chopping trees makes noise, which can attract mutants or other players. 'Stones' are gathered from rock formations using a 'Pickaxe'. Look for large boulders or rocky outcrops.
Once you have raw materials, you'll need to process them. 'Wood Logs' can be turned into 'Wood Planks' at a 'Sawmill' (found in industrial areas) or by crafting 'Wood Piles' at your base. 'Stones' can be crafted into 'Stone Piles'. You'll also need 'Metal Scraps' (found in industrial areas, junkyards, or by salvaging vehicles) and 'Nails' (found in residential areas or hardware stores) for various components. Always carry a 'Hammer' when building, as it's required to place and upgrade structures. Consider building a 'Storage Box' early on to safely store your gathered materials.