As soon as you enter the wasteland you can basically do this, there is no tutorial for how to build things but if you hold
button you go into construct mode. Once in this mode you can go up to things and hit
to gather materials.
Easiest way to get this is to build 100 Wooden Crates which are under the Furniture area, costs 3 wood to make 1 so essentially you will need 300 wood which is the easiest material to get.
Once you obtain enough materials just build 100 things and you will unlock this achievement.
This can take about 30 minutes to achievement which isn't that bad..