On my first elk hunt I was fortunate enough to go along with a very experienced elk hunter. We went to an area he knew well, packed in camp by horseback, nine miles from the road and up at about 9,000' in Wyoming.
I was in good shape, but used to living at about 1,000' above sea level, so it took me a few days to get used to the altitude. We scouted for elk, hiked and fished for a few days before the season. That was a good idea, as we located elk and got me used to living and working at altitude. Other posters have hit hard on the physical conditioning aspect of it - and I'd have to agree, at least for where I hunted. It's not only at high altitude, but it's doggone steep up there! Several days we did a LOT of hiking.
The area was NOT overrun with elk. We didn't see many, I did get a good clear shot at a nice 6x6 bull from about 180 yards and put him down with one 175 grain Nosler Partition from my 7mm Rem mag. My rifle was an inexpensive, off-the rack Rem 700 ADL that I'd done a trigger job on, and had shot a lot. It had a simple 3-9x Leupold, sighted-in at 300 yards. It's not the rifle, it's the shooter. Good bullets are a plus. I read a lot of posts from guys who swear that you need a half MOA rifle shooting 300 grain super slugs at warp speed. Not true, unless of course you're taking elk at a half mile or so. Most elk hunters I know use something like a .30-06 or .300 magnum with good 180 grain bullets. It's a pretty standard combo that works well. If you're pushing the long-range envelope, obviously a more specialized setup is nice.
Once the elk was down this deer hunter finally figured out how big those critters really are... My goodness... Standing there, on a steep hillside a mile or so from camp, at 10,000' up in the Wind River Mtns, with 700+ pounds of dead elk at my feet. I was a little overwhelmed. My buddy was the brains behind dismembering the carcass and he did a fine job of teaching me how it's done. After we had it apart, he headed back to camp for the horses and mules to pack it out, while I carried elk quarters down the mountain to the trail where the horses could reach them. This whole time we kept our rifles and big bore handguns available, as apparently the local grizzly population has learned that a gunshot can mean lunch. It took much of a day to get the elk skinned, quartered and back to camp. It took another day to get the elk nine miles down the trail to our trucks, then to drive the quarters & the head to the meat processor and the taxidermist, and then ride back into camp in a blowing snowstorm. Big day that was.
If you can't connect with a good local hunter, then I'd highly recommend going with a good, experienced outfitter. He'll have the knowledge and the tools to get the job done right. Although I haven't met him in person, I've heard good things about Lee Livingston who guides out of Cody Wyoming. We had a good conversation a couple of years ago about a backcountry mule deer hunt. That hunt fell through when I got hurt and couldn't do a backcountry hunt, so I didn't get to meet Lee in person. I'm sure there's a pile of other good guides too.
Since that hunt I've done some more elk hunting here in my home state of Washington, but not deep in the backcountry like that high altitude Wyoming trip.
Best of luck, do your research. By the way - if you want to hunt in Wyoming, you'll need to get your non-resident application in soon, I believe they're due in January.