First, the proper location must be found. You will receive a notification if you are in a HQ location. Tap down on the D-pad and select the "Relocate Home Base" option to move your crew out. Places that can be home bases are all totally fenced in and have gates, much like the church.
Locations that I've found:
McReady Farm: Located in almost the middle of the map; follow the road out of the first town and hang a left after the Veterinarian's office. This location is VERY remote. I am currently here, and I thought I could deal with the distance to civilization, but it is a lot harder than I thought. It is quite big though, and has a lot of space for improvements
The Alamo: A Fast food joint in downtown Marshall. It is right in the middle of the action, so you won't have to go far for scavenging missions, but it is also not very big. I think that most of the improvements are built on the roof.
House w/ Tree Fort: This one is introduced during the story, not sure if it can be found before then. It is also in Marshall, in the North/central area of town.
Actually, I'm not sure if you can move home base before the story allows.
Outposts create a safe zone around them that zombies don't spawn in and give you a resupply point in the field. Also, laying mines is awesome. They absolutely destroy and hordes following you into the Outpost safe zone.
Vehicles are finite, so you have to treat them carefully. I think the workshop may be bugged (at least in my game) as no weapons or vehicles ever autorepaired like it said they would.
Edited by TEoS, 06 June 2013 - 01:36 PM.