A technique that I've seen is to score the skin in strips on the outside and then cut and peel the skin like a band-aid with a sharp knife (paring or boning) aiding the separation. I'm not a butcher, but last time we cured meat, we (two people) went through 100 lbs of fresh meat meticulously in about 20 minutes using this method (the other person was a southern Italian gentleman who was an old-hand at this).
You use the knife to cut and separate the skin from the meat and end up with long strips of fat. The skin separates from the meat nicely if you work at the interface layer of the skin and the meat.
With fat, you do a similar method. Except this time you place the skin on the cutting board (fat side up) and essentially scrape the fat off the skin (almost like a fillet action).
In both cases, you grab the skin with one hand and use the knife to separate/wedge the skin from the meat/fat with the other (see the safety note below).
Important safety note: always make sure the knife blade is pointing away from you and you're "cutting away" from your body. Also make sure the hand that is holding the skin is behind the blade and not in the path. This is to make sure that if your hand and knife run away, injury does not occur.