Gybing is super easy, as long as you don't overcomplicate things.  Here are a few things people do that screw it up.

1) They try to use the wing to power though the gybe:   This usually ends up stalling the wing. Instead just let go of your back hand as soon as you start carving the board around.  Do NOT switch hands until you have carved all the way around and the board is pointing in the new direct.  Just get the wing out of the way by holding it over your head during the an manuver.  Once you are around, then change the hands over.  Free hand to the handle you are holding, and once you have it there, then move your old front hand to the back.

2)  They go into the gybe too slow.  If you go into the gybe to slow you wont have the momentum to carry you though the gybe.

3)  They head upwind before entering the gybe.  This slows you down and also makes you cover more ground in the gybe.  It takes less speed and energy to gybe on a downwind course.

Have a look at this video from the 96 seconds





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Gunnar

I am barely able to foil in both directions but did a successful gybe on my first attempt today.  I basically did what Gunnar describes (before reading this) because it is pretty intuitive.   Key is to have some speed so you can remain on foil.  As I started going down wind, I spun my wing towards me and kept turning my board, then grabbed wing in the other direction and rode away toeside.  I am not particularly athletic.