I first heard about this concept from a French hairdresser and thought it sounded a bit silly. After trying different ways to cut down my blow dry time, I came across this method again and decided to take a closer look. This looks like a method that needs some practice to perfect. How do you wrap your hair straight you ask? Well you start off with your hair damp, and begin sectioning it off just like you would to blow dry. Then you pull each piece to one side of your head. The idea is to pull your hair with some tension to straighten it out. Think of your hair after a sleek ponytail; the front gets super straight. So you use this same concept to straighten your entire hair.
I like to put a leave in conditioner or anything that is moisturizing but not too heavy.
Basically, wrap the hair like you would a scarf, starting from one side into a circular motion and securing the end with pins. For example, take the hair at the back of your head, pull it towards your ear and then up towards your forehead and secure. Once you are done with all the pieces, this will leave you with a section of hair on top of your head. Comb through this area to make it smooth. Using your thumb, press down on the hair on the crown, and then add it to the circle of already wrapped hairs. I admit it does look a bit funny when you go to bed. You can also sit under a dryer, or perhaps use your blow dryer to make it dry faster. 
The beauty of this method is that you aren’t damaging your hair with heat. I’m definitely going to practice this method so I can get the hang of it, and hopefully store away my blow dryer at least for the summer. You don't have to follow this exact method; as long as your hair has tension enough to straighten, you can come up with your own versions. 

Aline Agopian