Here is the inside-out braid on my oldest daughter. It works the best on her hair- since she actually has a real head of hair.
I typically braid with dry hair. It is easier for me to work with the dry hair as it doesn't tangle the ends and it stays nice and smooth. The only time I braid wet hair is if it is bedtime and we are going for a wavy look the next day.
I parted it like usual and started my braid up at the front, left side. By starting with a small section, this helps eliminate the huge bulky braid I had the last time. But this time, I only gathered hair from the bottom side (last time I gathered from the top and bottom.) This turned the braid inside-out. (I will post videos as soon as I can get my computer to read the video file. I am having issues with that.) Once again, make sure the hair is already combed the way you want it going. I ended the braid early, pulled back the hair from the front of the other side and stuck a big flower in. It took less than 5 minutes.