Main Walkthrough

Location: Gusu City
Petitioner: Liu Cheng the Blacksmith
Prerequisites: Complete Sword Appreciation Assembly
Reward: Longyuan Sword

In order to trigger this quest you need to first complete Sword Appreciation Assembly, the main story quest that first takes you to Mingjian Manor from Gusu City. Once that's done you can trigger Forging with Winterspring by speaking to Liu Cheng, Gusu's blacksmith.

Liu Cheng has trouble. His father had a dream of crafting a powerful sword, but he needed Winterspring Water, which could only be procured from Mingjian Manor. Alas, the elders of the manor wouldn't grant the request, and Cheng is left to worry about his legacy. Agree to help and Yi will need to speak to them on Liu Cheng's behalf.

Travel to Mingjian Manor. There are three halls in the north of the manor grounds, and you want Gan Jiang Hall, the western building. Inside and on your left you'll find Ouyang Maocai. He's only willing to part with Winterspring if you bring him Siderite Ore. Siderite is arguably the rarest of the ores in Wandering Sword. Normally you have to wait a while to claim any Siderite Ore, assuming you want to harvest it naturally. 

Fortunately, there is one source available immediately after you finish with Gusu City. Travel west of Gusu City and you'll find a dungeon known as Mount Tigeroar. If you travel all the way through Mount Tigeroar, into the cave and all the way to the west, you'll find a unique enemy named Wang Meng the Winged Tiger. He's guarding a chest that you can't open without defeating him. Do so and you can claim the contents of the chest, including a piece of Siderite Ore.

(If that chest for some reason isn't available, wait until you have access to the Outer Lands, the deserts in the north. If you travel as far east as you can go you'll find a snowy area, with a place called Mount Tianshan. There are some ore deposits on this mountain that you can use.)

Bring the Siderite Ore to Ouyang Maocai and he'll trade you for some Winterspring. Take this to Liu Cheng and he'll tell you to return after a few days. Wandering the world map and entering another location should do it. (I traveled to Tancheng City and back. Worked fine.) Speak to Liu Cheng again to receive your reward.