Plate Mail is crafted with Blacksmithing in Mabinogi (armor). 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 8 and survives 30 uses; every crafting attempt spends one use.
Fleta: wandering NPC. Sen Mag Plains crossroads, morning/afternoon/evening windows (93,000 gold).
Desert Dragon: field raid boss at Sheep Landmark in Rano. Dagger, Cuirassier Helm, and Dragon Shield manuals in the raid loot. No requirements; fight it at the Sheep Landmark in Rano during twice-daily spawn windows.
Lileas: Jousting Arena Manager in Tara. Trade Jousting Points at her shop for manuals (93,000 gold). Spend Jousting Points at Lileas's shop by the Tara jousting arena, earned from matches there.
Materials
Expect about 8 attempts per finished item (14% average progress per attempt). Per-attempt materials are consumed on every attempt; finishing materials once per item.
Each attempt uses
4× Iron Ingot — refine from Iron Ore (common low-rank Refining output)
3× Fine Leather Strap — weaving rank 6 on a spinning wheel
2× Braid — low-rank Weaving skill output
Finishing (once per item)
1× Fine Fabric — weaving on a loom, low rank
1× Siren's Bat Wing Mask — Siren monster drop in Rundal Dungeon