Prerequisites: Max out Runeheart's level 1 friendship
Reward: None
Unlocks: Runeheart level 2 friendship, A Promising Successor
The younger of Moonbury's two blacksmiths, Runeheart can usually be found at the Hearts and Sparks Shop, where she works with her mother Opalheart. They also have a home just south of Town Hall, if you can't find her there. Lacking that Runeheart wanders Moonbury, though she seems to particularly like the park to the south of the Hearts and Sparks Shop. Seek her out in any of these locations to raise your friendship with her.
Once you've maxed out Runeheart's first level friendship you'll see a message on Moonbury's Bulletin Boards directing you to the Hearts and Sparks Shop. Go there and you'll find mother and daughter blacksmith arguing with each other, and Runeheart will storm off. You'll need to go to the Lazy Bowl Tavern between 19:00 and 23:00 - pretty late in the day, in other words - to see how Runeheart is doing.
Runeheart is angrily playing darts when you enter the Tavern, and she'll vent about her mother a bit before calming down. Talk to her a bit will end the quest with the two of you on better terms - and at the beginning of the second tier of your friendship. All done. Bump this level of relationship to the max and you'll reach the next quest in Runeheart's line, A Promising Successor.