You might be used to overly complicated tasks, but for once this isn't one of them. Unfortunately, this doesn't mean that it's going to be an easy task. If you're struggling, then our The Last Stand: Aftermath The Others Task Guide will teach you how to finish the task without dying.
The Last Stand: Aftermath The Others Task Guide
This is a very simple task in all honesty. You arrive in the middle of a crowd of zombies, with almost no warning. If you've got any beeper bombs or other devices to attract the zombies, you might want to throw them so you don't get immediately overwhelmed. Other than that, you need to rely on your skill to manage the horde effectively. Keep moving, keep firing, and make sure you don't get tagged by one of the exploding zeds because that can basically be a down in one sort of move.
Once you've finally cleared them all out, you can go and talk to the guy at the gate to be allowed into the compound.

So you can now explore this classic piece of apocalypse architecture and scavenge resources from it. For whatever reason, these guys don't seem to have a big problem with you just stealing all of their stuff, even before you've really spoken to them about it. You can even find some better resources here than you'll normally find anywhere else that you've been to already.
Explore the structure until you come across the Lord Humungous-looking git and converse with him. There's a lot of back and forth between you two, but eventually, he allows you passage into his domain. From now on, if you go for a stronghold in this area it'll be here in the compound.