As simple as clearing out infestations in each zone.
It's wise to stock up on ammo before heading out, take lots of explosives and make sure you have saddle ammo sacks (The second upgrade at least.) Sometimes a Horde is attracted by the fires and the gunshots of killing the enemies pouring out the nest as it burns. Which is why it's best to take explosives and later on you can set up perimeter's using land mines if you don't fancy being caught out.
The last set are Crier nests and appear as an "optional" objective. You can get away with using one molotov on some of these. Where two are on adjacent branches, hit one of the as close to the tree trunk as possible. Hitting the trunk can often result in nothing being set on fire.
Crier nests appear only in The Southern Regions (Highway 79 and Crater).