To rough butcher a hog in the field, load the coolers with ice before you start, so once you're done, the meat doesn't spoil in a hot cooler while you're riding around looking for a country store.
Skin and dress the pig like just like you would a deer, then start cutting. This is a quick, minimal approach, so keep it as clean as possible. Wipe all sawed bone with a wet towel to remove any bone meal and chips before chunking meat in the coolers.
Once the animal is gutted and skinned, saw off the front legs just below the still-attached hide, and remove the shoulders. You don't need a saw for this. Just push back on the front quarter and cut between the shoulder blade and ribs.
Bacon comes from the hog's sidemeat. Even if you don't plan on curing it, save this precious cut for strips of seasoning meat for summer veggies.
For a double rack of ribs, saw off the rib cage on each side, leaving 4 inches of rib stubs connected to the backbone.
Now, saw through the hog's back at the base of the rib cage. You'll have a massive rack of chops. Toss the whole thing in the cooler. Later, you can saw straight through the middle of the backbone, and then separate the ribs for hog chops.
Saw through the backbone at the hip joint for a loin roast, and split the hams.