"skip shifting" ? Never heard of it, but I'm assuming you mean skipping a gear while shifting. For instance, going downhill you might skip a gear or two....easy, just shift from 3rd to 5th or whatever.
Just like it sounds. You skip a gear in the sequence. As you've probably already learned, shift points are tied to speed/gear/rpm combinations. IOW, a given truck with a given drive train will go x mph in y gear at z rpm every time. None of that changes with skip shifting. What changes is your shift points. For downshifting, you allow the rpm & speed to drop below your 'standard' shift point and then shift as normal i.e. to neutral, goose the pedal to rev the RPM's up, then shift to the lower gear except in this case the lower gear is two gears lower instead of one because you've allowed the speed/rpm to decrease lower than what your instructor probably taught you in school. Skip shifting on the upshift works the same way. But you'll generally only do it when hills are involved or you're extremely light because otherwise it would require reving the engine pretty high and you'll want to avoid that for lots of reasons. As for pros and cons, I think its entirely debatable. Once you're on your own, you'll work yourself into a groove and you'll figure out when you like to do it and when you don't. I wouldn't really worry about it too much beyond that. Every transmission is different so there are no hard fast rules as far as speed/rpm/gear go. The truck will tell you when you've let the rpm get too low and you'll figure out when you can skip gears when you can't as you go.
I only skip shift when I bobtail. I drive my lightning 10 as a 5 speed. Actually as a 4 speed as I start in 3rd (2nd lever position) and only move the lever 4 times.
Idk about the cons of skip shifting.. then again the my only pro for it is one less gear to shift but i dont know. I usually only skip shift under light loads or bobtail. Always skip a couple of gears down shifting.. but that is the way I drive. If you skip, then great. All about how comfortable you feel with shifting. *123456 Merry Christmas! (Same goes to y'all as well)