The pattern I'm using is Butterick B6229 from their Making History series. It includes a dress, the apron, and headpiece. I'm only creating the apron for my project.
Several years ago I found a bolt of 118" wide cotton sateen. I love sateen for linings of jackets and skirts and it is smooth and doesn't catch on other fabrics. It can also be used alone and easily dyes. I'm at the end of the bolt and will have to deal with the residue of the manufacturer's tape but that's easily cut around.
The first step in creating this apron is to make the tucks in the bib. The fabric is folded at the foldline marked on the pattern and then stitched a distance from the fold as marked on the pattern. After stitching, the thread line is pressed to integrate the thread into the fabric. Then the entire fold is pressed into the correct position which for this apron is down.
Similar to sewing in the ruffled lace, the bib is machine sewn to the strap on the side that will face out, and then the facing is hand stitched closed on the side that will face in.