Joshua, Heres what I would recomend.
First start researching all the states for special draw hunts. Eastmans hunting journal usually has a members research section once a year that really explains each state and how they conduct hunts. For example KY now has an elk hunt every year and you can apply online for $10 and it take all of 5 minutes. Those special draw hunts are where you will make big money if you get drawn,, but are hard to get drawn.
In the meantime though I would start planning a trip to Colorado. They have the largest Elk population and are the most friendly towards non-resident hunters(ie some of the hunts do not require special draw for non-res). then start doing some homework on good areas of national forest that you can hunt. Wildreness areas and Roadless areas are a good start.
Next step is to take a vacation. I would recomend going to that area in the summer and having a little camping trip. Check the area out, look for sign, get comfortable with the lay of the land. if it doesnt look promising pack up and head to a back-up location you have selected. You can do a little trip like this fairly cheap if you drive and it is a hell of alot of fun to get out in the hills and camp for a few days. It will sure pay off to when season rolls around.
Once you have an area selected get a map. I get the topo kind with an overlay of picture, you can find them at mytopo.com. the maps arent cheap but so worth it. when you get your map you can use state websites to determine location of private land, roads, streams,etc, etc. I draw all that stuff in on my map.
After that, mark some time off and just go! I think alot of folks think you need to have an outfitter to elk hunt. absolutely not! the trade off is two fold though. first you need to do a ton of homework(great way to kill time in the off season) by prepping maps, getting the right gear, etc.
The second thing is get ready to work your *** off. Not having horses that an outfitter provides sucks but it just means you need to put boots to ground. So get in shape and be ready to walk a long ways and ready to pack an Elk out on your back if you get one.
Its all very doable just means you have to work a good deal to make it happen. tons of guys on here do this very thing and are every bit as successful as outfitted hunts. Personally i get a great deal of satisfaction out pulling off this kind of hunt, even if i dont get something. Its nothing against guides or taking guided hunts but I just love the acomplishment of going and surviving out in the mountains without any assistance.
I hope this helped a bit and let me know if you have any questions, i know i was pretty broad with what I wrote.
Get ready to be addicted to Elk hunting!