But like any RPG, you go around talking to people. Things will come up.
Yeah, this is pretty much the thing to do if you want to find side quests.
Some quests are unmarked, so you might have to use the wiki to find some of those in later playthroughs, but for now, just look for new areas and then talk to all of the people in those areas. Someone is bound to have some kind of problem that they need help with. Oh, and a lot of sidequests can only be accessed/finished if you have certain skills at certain levels, so watch out for skill checks in dialogue and know that if you don't pass them, you may be unable to start a particular quest until you pass them.