For field dressing pigs, I cut just under the skin down the side of the penis, scrotum then around the anus, taking care to not cut any of the intestine, urethra, etc. Then I cut just under the skin up to the breastbone then under the breastbone up to the throat area, under the chin. I reach in and grab all the tubes, veins, arteries and cut them. Then, I just pull everything out. It all comes out connected, in one big pile and you are left with the empty carcass. I wash it out with a gallon of water I have remembered to bring along. Then, when I get the pig back to camp, I hang it, skin it, take a Sawzall, quarter it, then put it in a large cooler with ice.
I only keep the loins whole. The rest I take to a processor to be ground up into bulk sausage. I have a stuffer to make my own links.