From the map screen, you can freely attack towns and camps by selecting them and clicking Attack. The only exceptions are towns owned by the FSA and Republic of Arizona. The wealth rating of each settlement gives an idea of how much can be looted, while the defense score shows what kind of resistance to expect.

From the missions window you can follow the story by completing chapter missions, or you can complete randomly generated missions. Just click accept after selecting a mission.

From the item window you can buy new weapons and armor. At first not much will be available, so you'll have to build up your reputation. Items are not guaranteed to remain in the market forever, so if you see something you really want, make sure to get it quickly.