RE: First time Elk Hunt
You really need to increase your lung capacity if you're going to be hunting at high elevation so that you can hold more oxygen. Quite possibly the best way to do this is swimming laps. When you swim laps and push yourself hard, you are forced to hold your breath while still exerting energy, so your lung capacity is increased faster than it is doing activities like running. You also need to run/jog to get your legs into shape too, though, so don't rely on swimming alone to prepare you.
Almost forgot, you can increase your recovery time by running at say 50% speed for about 125yrds then sprinting full speed for about 50 yrds. Run like this for about ten minutes a night, and you will be amazed at how fast you can recover after a grueling walk up a mountain. This is one of the ways we get into shape for soccer, but I can assure you it works just as good for hunting.