Good advice so far. "Get in great shape." Of course, if you aren't already far down this road I don't see how you are going to get there in a month. Let's hope this didn't sneak up on you. Be in good shape; have your weight way down where it ought to be. Endurance and stamina are the most important ingredients of the "be in shape" admonition. Running and other cardiovascular oriented exercise help a lot to build this stamina. If you want to work on strength IN ADDITION TO CARDIO work on your legs. Do squats with weights. Do lunges. Climb lots of stairs. If you want to work additional strength, work on your core with sit-ups, crunches and something to strengthen your back.
I have gone to the mountains many times. Often I go from my 600 foot elevation to 7000 foot elevation and sleep on day 1 and am out at 9000 feet working hard on day 2 and heading towards higher ground under a heavy pack -- sleeping at 12000 feet on day 3 -- with no ill effects. Even so, I had something once I think was altitude sickness and it wasn't fun, and it wasn't all that high elevation -- 9,500 feet? I think I overworked myself on this one occasion, then again maybe it was some sort of virus.
If you can get a couple of days sleeping at some higher elevation -- 6000 feet, 8000 feet -- this is good. If you can avoid really busting your butt the first day, that might be good too. I have heard -- from my personal physician just last week -- that Tums can help avoid altitude sickness. Look at the active ingredient in Tums -- this is the key. I think it is like baking soda or something like that -- alkyline. No doubt other substances help as well.
If you do get altitude sickness, in the Rocky Mountains you aren't likely to experience any truly dangerous effects, but you might feel badly. Even if you are in shape, expect to get easily winded. Don't try to run a marathon out there. Walk and hike at a pace which suits you. Don't be afraid to stop to catch your breath. Good luck.