For my Dutch readers: the same tutorial is available in Dutch here.
1. Basic pieces: the sleeve (in my pictures a piece of cotton that was near) and a rectangle 4 cm wide for the slit facing at least twice as long as the length of the slit. My piece is a bit longer because I find it easier to work that way.
2. Pin the sleeve on the facing, right sides together. The ends are matching, the middle corner is 0.5 cm from the edge. Fold the sleeve in a way that no real fold is made.
3. Stitch 0.5 cm from the edge. At the center the stitches just touch the fabric of the sleeve. 
4. Press the seams towards the opening
5. Press a seam in the split facing
6. Fold and stitch-in-the-ditch from the right side of the sleeve. This is hardly visible if you do it in matching thread. My black on white is only for these pictures ;) 
This is the way the inside looks now: 
7. Stitch a diagonal line at the top of the facing. This will prevent stress on the weakest part of the construction.
8. Fold one side inwards (on the side of the widest part of the sleeve) and press.
Ready! It doesn’t take long, but don’t forget to press in different stages for a neat result. 
