You increase your attributes and earn wealth by completing adventures, which usually begin in settlements. Rolling intelligence against d8 reveals some detail about the adventure, such as what type of enemies you might face or what kits could be useful. Rolling charisma against d8 increases the wealth reward by 1. Each character may attempt each of these rolls once per adventure.
A successful adventure always increases your team's wealth by at least 1. You could earn a variety of other, less-tangible rewards, too, things like allies, fame, or titles. Of course, you could also find new equipment depending on what types of challenges and enemies you faced during the adventure.