I looked into making a sleeve placket when a BurdaStyle shirt pattern I was using turned out not to have one. It turns out it's easy to make a professional-looking sleeve placket. This tutorial is easily adapted to make plackets of all sizes.
If your pattern does not come with a placket piece, here is a video where I show you how to draft a pattern piece. All you need is paper, a ruler and a pencil.
Now follow the steps below to sew it up.
Fold the sides and the triangular bit at the top of the placket piece 1/4" to the wrong side and iron. Place the RIGHT side of the placket on the WRONG side of sleeve pattern piece, lining up the cutting lines and pin in place.
Sew along the stitching line. Use a short stitch length in the corners for accuracy. Cut most of the way up the cutting line and into the corners. Cut carefully and as close into the corners as possible without slicing through the thread.
Press the seams open and turn the placket to the right side of the sleeve, pressing again to make the opening nice and crisp.
Fold the shorter side into the vent so that the folded edge just covers the stitching line, with the raw edge enclosed and pin in place.
Topstitch. This is where an edge stitch foot would come in really handy.
Fold the larger side of the placket in the same fashion, with the folded edge just covering the stitches and the placket covering the vent and the other half of the placket, the raw edges enclosed. Pin in place, including a pin marking the top of the vent opening.
Topstitch the side and top edge of the placket, partway down the other side and back across the placket, just above the vent opening. Use an edge stitching foot if you have one. Press