In this recipe in minute 7:00 the cook separates the chicken skin from the breast to put butter between the skin and the breast for basting. When I tried that (very slowly) it always felt like I was about to rip the skin. When I finished a sizable part of the breast was left exposed because some of the skin ripped.
I'd say experience ?
You need to try it a few times to get the feel of the skin and the meat and how much pressure is needed to separate the skin from the meat.
Try putting more pressure on the meat itself and not on the skin (hard to describe).
The quality of the chicken is also important, most supermarket chicken have crappy skin and will break easily.
If you try on a good free-range chicken, the skin will be sturdier (personal experience, here).