Location: Tancheng City
Petitioner: Hong the Innkeeper
Reward: Dragon Boat Mandarin Fish Recipe, Martial Arts Notes, 2,000 coins
To trigger this side quest you first need to find your way to Tancheng City. It's located to the south of Pingkang City and the general starting area of the game. Head south until you see a waterfall, then cross the nearest bridge and keep going south a ways until you see a settlement on your right. This is Tancheng City.
The petitioner for this quest is Hong, the owner of Tancheng's inn. You'll find the inn in the northwest of Tancheng City. He's annoyed about the fee needed to get into the Clean Clothing Faction of the Beggars' Sect, as well as the requirement of an 'exotic' item. He asks Yi to go check out the Solitary Marsh Cloud Pier, where a merchant with exotic wares is said to be staying.
Leave Tancheng City and walk southwest. Just before you run into a mountain range you'll find the edge of a river, and the Solitary Marsh Cloud Pier is between the mountain range and the river. Check the lower level of the pier and you'll find a Merchant, standing west of the stairs, who has some... interesting items. He'll sell Yi a Thousand-Year-Old Centipede Skin.
Take the skin back to Hong and he'll hand over your reward, as well as outline the functions of the Beggars' Guild. Educational.