Fine Anvil is crafted with Blacksmithing in Mabinogi. This page lists everything needed to make it, checked against the game as it exists today. The interactive planner lives in the Blacksmith Companion.
How to get the manual
The manual is rank 9 and survives 30 uses; every crafting attempt spends one use.
Lorraine: General Store owner in Dugald Marketplace. Sells Furnace manuals directly in her shop (12,700 gold).
Elain: storekeeper's shop in Sen Mag Marketplace. Sells furnace/anvil blacksmithing manuals (12,700 gold).
Ailbhis: general store worker in Abb Neagh Marketplace, Stump Square. Sells furnace/anvil blacksmithing manuals (12,700 gold).
Lileas: Jousting Arena Manager in Tara. Trade Jousting Points at her shop for manuals (12,700 gold). Spend Jousting Points at Lileas's shop by the Tara jousting arena, earned from matches there.
Materials
Expect about 2 attempts per finished item (70% average progress per attempt). Per-attempt materials are consumed on every attempt; finishing materials once per item.
Each attempt uses
4× Castle Building Stones — buy from Lorraine/Elain/Ailbhis/Marcellus building-stone shops
3× Iron Plate — refine from Iron Ingot (re-refining)