To trigger this quest you need to spend some time in the Mines. You’ll find them in the northeast of Pelican Town, at the end of the river that meanders north and south through the east side of town. You won’t be able to access the Mines at first, and it’s possible (though I’m not positive about this) that you won’t be able to get in until you reach Summer.

Upon entering the Mines you’ll find Marlon, an old warrior, who will want to see you how well you fare in the depths. He’ll give you a Rusty Sword, which will then activate the quest Explore the Mines. The Mines will be described at greater detail in another article, but for the moment the following advice will suffice:
  • Each floor of the Mines is inhabited by a mixture of rocks, valuable resources, and monsters. The floors get larger and the monsters deadlier as you descend.
  • To get to the next floor you need to find a ladder. They’re secreted beneath the rocks, requiring some Pick Axing work. You can also sometimes find a ladder by killing enemies.
  • Monsters will hurt you. Use the Sword, like any other tool, to kill them off. Bring food items to restore Health and Energy alike.
While exploring the Mines you’ll come across nasty little Slimes which attack by hurtling themselves at you. Not too difficult. Kill at least one Slime (they’ll start appearing on the second floor and below), then go home and nap. The next day you’ll get a letter which triggers this quest.

The rest of the quest is pretty simple: kill ten more Slimes. Explore the Mines at greater length to get the job done. Once you’ve killed the lot you’ll unlock the Adventurer’s Guild, which is located right outside the Mine. Here you can trick yourself out with better adventuring gear, as well as earn rewards for killing monsters. Huzzah!