Press up on the D-pad, go to the very right to see your home and there should be an empty spot on the floor map where you can start building a workshop if you have enough materials.
To get materials, you need to search either houses but mostly when you come across garage shacks or warehouses where as you're searching, the question marks will turn into the round balls material icon. It's usually in a crate and you'll have the option to radio home, where then you can call a scavenger to pick up the materials. Be wary if the place you've found for materials is far away, the scavenger could be set upon by zombies and you'll have to manually escort him the way back to make sure he gets back home.