You can obtain quests by talking to the NPCs around town. Most of the quests involve you simply bringing them an item that they're looking for. Some get a little bit more elaborate than that, but not by much.

Just talk to the NPCs and they'll ask you to bring something to them, animal glue, a cornette, whatever.

I suggest talking to the S.O.B gang behind the warehouses in Port Wind cause they'll give you quests that reward you with some good stuff. Justice Badge and Blaze Spikes for example.