Open your map screen and highlight a particular site. To help your search, each site you’ve seen (either close up or by surveying from a high point) shows the kind of resources you’re likely to find.
Usually, you’ll gather these supplies by scavenging whatever’s been left behind at the various buildings around town. The resource you’ll need most often for facility management is materials, but facility actions and upgrades could also require meds, parts, or many other kinds of supplies. Facility construction, actions, and upgrades all require supplies.