While you can collect most resources from buildings in your facility, Neutronium can only be gathered from meteors and by building outposts on Neutronium Veins on the world map! There are also many other deposits of other resources available on the World Map.
Simply tap the resource you want to collect and tap Gather. Choose a starting location, an available dropship, and troops you want to deploy. The more troops you send, the more resources you'll be able to gather in one trip.