You will need:
A pattern- either buy a pattern (my favorite sources are Wearable Quilts and the SCA)
Lots of Pieceables
Step 1: Get Supplies- Pattern and Pieceables
Once you have your pattern you can figure out how many Pieceables you need one per 2 square inches in theory. In practice I feel that it is closer to 3 square inches as they overlap around the edges so small pieces use very little to go a long way.
Step 2: Begin Snapping Pieceables Together
I like to snap mine together in rows. Once you have enough for gauntlets (20-40 depending on arm size), simply snap in the back. the more connections you have, the sturdier the construction. Think like building a house, more reinforcement is good.
You can also make a bracelet to give you a feel for size.
Step 3: Practice Bracelet
Step 4: Make the Vest
What will you make?