Apron Dress is crafted with Tailoring in Mabinogi (clothes). This page lists everything needed to make it, checked against the game as it exists today. The interactive planner lives in the Tailoring Companion.
How to get the sewing pattern
The sewing pattern is rank 2 and survives 30 uses; every crafting attempt spends one use.
Purify Avalon's Shore: Queue for this purification mission and defeat Archelon on Avalon Shore for a chance at tailoring manuals.. Open a Purification Board and select this mission to enter with a party.
Sources that no longer exist: Production Gachapon (2012).
Materials
Expect about 6 attempts per finished item (17% average progress per attempt). Per-attempt materials are consumed on every attempt; finishing materials once per item.
Each attempt uses
5× Finest Fabric — weaving on a loom, higher rank
5× Finest Silk — weaving on a loom, higher rank
2× Fine Fabric — weaving on a loom, low rank
Finishing (once per item)
4× Finest Finishing Thread — Buy directly from any general goods NPC shop.