Location: Boklad
Petitioner: Kveta, Porter
Unlocked: Complete most of Onward
Reward: 20 Wyrrite, 1 Meteorite, 30 Renown, 800 gil
In order to unlock this side quest you must first complete almost all of Onward, a main story quest that will take you to the border town of Boklad. This involves completing two sub-quests and retrieving a Trader's Pass from some bandits. Once you have the Trader's Pass you're meant to speak to Goetz in Boklad. At this point you'll unlock three side quests in Boklad, including Live and Let Live.
You'll find Kveta, the petitioner for this quest, at the south end of Boklad's central intersection. Kveta's things are being actively burgled, and the sellsword she hired to deal with the problem has disappeared. She wants Clive to look for the missing Josef.
Head south through Boklad and you'll see a Refugee on your left. She saw a man of Josef's description, further down the road. Leave Boklad and head to the Steps of the Forgotten, following the main road until you see a Chocobo off to your right. Beside it is another Refugee, and her son will point you up into the western hills.
Climb the rocks to the west and make your way into the cave labelled Mekith. Inside is a goblin encampment, and a Goblin Prince will step up to challenge Clive. Despite being slightly more challenging than the average goblin - and possessing far more HP, to boot - this little guy is nothing to your group. Beat the snot out of him with Eikonic Abilities.
You'll receive a Goblin Coin for defeating the Goblin Prince. Josef will show up after the battle to explain the situation, and you can return to Kveta to wrap up the quest.