All quests unrelated to the main quest are randomly generated. There are 4 types of side quests in Arena.
Rescue Shuckeki from the Wharf Rats (Quest giver: Princess Modk, Belkarth Guard Palace. Talk to the princess, go to random dungeon location, rescue the princess' sister, escort her back to Belkarth Guard)
Test-tube of chemicals (Quest giver: Inn-keeper Golden Pit, Belkarth Guard. Run to the mage's guild, talk to the wizard there, run back to Golden Pit, talk to the inn-keeper)
Important letter (Quest giver: Inn-keeper White Griffn, Belkarth Guard. Run to Buv's Quality Weaponry Store, talk to the blacksmith, run back to White Griffin, talk to the inn-keeper)