1. You first field dress it - cut from sternum to tail and pull the entrails, leaving them in a pile in the woods for scavengers. That takes your elk from 700 lbs (you hope) to ~450 lbs.
2. Quarter it and hang the 4 ~100lbs quarters high in a tree safe from bears and wolves (but not cougars) and carry them out one at a time using a backpack with a frame and hip belt. Be sure to carry the prime cuts (backstraps) out with the first load. Watch for predators on the return trips.
3. It's becoming more common, too, to fully butcher the animal in the field, removing the bones, which reduces the load to haul down to about 200 lbs. The skin, ivory, and head (if you want those) add some weight.
A Jet Sled in 2" of snow makes it surprisingly easy to haul an awful lot of elk and gear. As long as you're going across flat ground or downhill, that is - uphill is no fun at all.
A whitetail here in Michigan is much easier, even a big one is only about 100 lbs after field dressing. You just lay it on a drag/tarp or in a sled (or, if you don't care about the skin staying pristine and aren't going over super rocky terrain, just tie a rope to the antlers and front legs) and drag it out.
The big goal is to not puncture intestines, as they are gross and contain bacteria that will spoil the meat.
To skin it, I started at a back leg, just making a cut, pulling the skin up, and seeing it's connected to muscle by very soft fat. You can pull on the skin, slice the fat, and the animal basically unwraps. You want to keep hair off the meat because again, bacteria.
Front quarters are easy as there's no bone joint. They pop off quckly. Rear are harder, you need to find and cut the ligament(?) that holds the leg in the hip.
Then, I put about half the elk on a children's sled, and pulled it (mercifully downhill or level) about 1.5 miles. Then, I went and got the other half. She was a cow, so no antlers to carry.
Then, I hung all the meat in a frienda garage for about 2 days, took it home in several coolers, and fought off my dog while every evening for 4 evenings, I separated the muscle groups, and/or chunked meat to grind (lower quality meat gets turned into hamburger or sausage), vacuum sealed eveything, and froze it.
I'm originally from Rhode Island, and this is only my third animal (first was a deer, then an antelope) so it was pretty overwhelming.