Cuff from a DVF Julian dress. Note where the cuff vent starts, about an inch down from the cuff/sleeve seam. The cuff is finished on the inside in a very neat way that hides all the seam allowances.
Inside out, the inner cuff seam allowance has been folded under and stiched in the ditch from the right side, which is the line of stitching you see here. In the previous photo the ditch stitching goes exactly down the cuff/sleeve seam so you don't see it from the right side.
Cuff pattern piece, a piece of tricot fusible has been applied already. Fold line is in the middle going from left to right, I used a 5/8" seam allowance but you could use smaller, like 1/4"
Fold the piece crosswise, matching ends
Mark the distance you want the cuff vent to start from the foldline. (See 1st image to see what I'm talking about) You can see two faint blue marks here, the cuff ends will have an opening from the center foldline to that point.
Stitch from the outer edges to the mark on both sides. Backstitch at the mark, but it's not necessary going off the edge
Lining up the fabric for the next part is a bit tricky, easiest way to visualize it is to pick up the top layer like I have here, then pull the bottom layer in the opposite direction with your other hand.
The north and south parts are sewn already, the west (in my hand) and east parts are lined up ready to be sewn.
Fold the N and S parts off to the right, and pin them out of the way. It's important to line up the end of the stitching so this next stitching line will end exactly where the last one left off. You can feel it one on top of the other when it's right, then pin. Sew from the end on the left side (which will become the point of the cuff) exactly to the beginning of the last stitching. Do not stop short or go past it. I find it easier to begin stitching in the center and sew towards either end, backstitching at the ends only.
Now fold the N and S parts to the left, and sew the other side the same as the first.
All four corners are now sewn, the stitching for each of them should all end at the same point.
Press, trim, and clip your seam allowances, then turn the whole thing right side out, using a point presser or similar to get the points out.
You can use either side of the cuff for the outside, whichever one you choose pin it right sides together to the sleeve. You will have to fold the other half of the cuff out of the way. Sew the seam, then press and trim seam allowances.
Turn the sleeve inside out (as shown here) and press the allowances toward the cuff (away from the sleeve).
Fold and press the inner cuff into place, tucking the seam allowance under and lining up the edge with the stitching line from sewing the outer cuff. It takes a bit of practice to line this up properly, you need some overhang to make sure the stitching catches this fold. Once it's pressed and pinned, stitch in the ditch from the right side, trying to get the needle to go right down the seam. This is what it looks like from the inside. From the outside it looks like the first photo, you shouldn't see the stitching from attaching the inner cuff.