I can add a few hints that may be helpful.
Experienced tailors know to insert the needle from the underside, but if you're just learning, it's easy to confuse the buttonhole stitch with a blanket stitch.
The keyhole buttonhole is for tailored garments; in dressmaking you frequently use straight buttonholes and a fine silk thread.
After waxing the thread, put it between two paper towels and press so the wax melts into the fibers. It will be easier to handle and the wax won't rub off as you make the stitches. I wax and press several yards at the outset and wind it onto a spool for use as needed.
To reduce fraying at the opening, use a small knife, heat, and beeswax to seal the edges.Hold the buttonhole with wrong sides together and both cut edges on top. I warm the knife with a hot iron, quickly rub it over the beeswax, then rub it over the edges. Lastly,I overcast the edges if needed.
When making the stitch, begin by holding both threads close to the needle eye. Slide your fingers away from the needle until you have enough thread to wrap it under the needle point in the direction you are going. If you keep this in mind you can work top to bottom, vice versa, right to left or left to right. I realize that old-school tailors will work in only one direction but if you are left handed or learning these directions will be helpful.
The stitches around the buttonhole can be used as a guide for the depth of the buttonhole stitches and the closeness. I have to work to avoid crowding my stitches.
When I teach thread buttonholes, I teach the stitch first; it's a waste of time to try to make a buttonhole before your stitch is perfect.