To being turning your ball of yarn into a hank, just start winding the yarn around the chair back.
You want to wind the yarn tightly enough that it stays up on the back of the chair, but not so tightly that you're over tensioning the yarn. It should still look a little wavy as it sits on the chair.
You can hold onto the ball of yarn as you work if you like, or just let it roll around in the chair. It will likely fall to the floor at some point, but that's no problem unless you have cats around.