Conditioning, to me, means endurance, not power. Many routes steadily sap away your strength so that, once the burn takes over, easy moves feel impossible. How frustrating it is to have passed the so-called crux, but not be able to hang on to finish! An indoor wall is perfect for building the necessary stamina in two fundamental ways. Pushing your muscles to fatigue will certainly help endurance, but equally important is learning how to rest.
Imagine a tachometer on each forearm. When you arrive at the practice rest stance, you might be"red-lining," feeling that you simply can't hold on any longer. Here's where the brain kicks in. Don't let go. Give one arm a quick reprieve then rest the other. The tachometer reading might continue to increase for a moment, before this back-and-forth alternation of rests begins to work. Don't give up. Those RPM's will drop if you persevere.
As the fatigue lessens, increase the rest time for each side. Slow down your breathing. Think about subtle shifts in hip or foot positions to further take weight off your arms. Be patient. Know that you CAN squeeze a rest out of almost any position along the route. Climbers burn out mainly because they don't have faith in their capacity to make a full recovery. As you get stronger and smarter as a climber, you'll keep an eye on that imaginary tachometer, and if you can learn how to keep it off the red line in the first place, the comeback will be quicker and more complete.
As your ability to rest improves, you'll notice that you can milk a rest out of almost any position, even while you are climbing. As one part of the body is straining, the others have been taught how to disengage. Even overhanging terrain can be restfully climbed in kind of a swimming motion, with the tiring arm dropping just for a moment of relaxation before reaching up to relieve the other arm. There's no point keeping both arms working at the same time. I strongly disagree with the adage that one must climb quickly through a crux in order to preserve energy. Instead, you should "top off" the tank at every possible moment, weasling some kind of rest between every single move.
Specifically, an open-handed grip is more restful than a crimp. And a jam is far more restful than either. Get good at both. Then ask experienced climbers to explain some of the more clever rests, like knee-bars.
Finally, do not let yourself get hurt during training. Quit at the slightest hint of joint or tendon pain. A broad, muscle-centered burn is fine. A focused tendon or joint injury is very different. Elbow tendinitis in climbers can take over a year to mend.
As for exercises you can do outside of the wall? A million light pull-downs on a lat machine will help. Remember, you are looking for the slow burn, to approximate the feeling of fatigue you experienced during your last melt-down. Accordingly, doing pull-ups while standing on a chair positioned back a few feet (to approximate the body position on an overhang) can work wonders. Yes, cheating with the chair will make it seem foolishly easy at first, but when the flame ignites, first in your arms, then in your legs, you can close your eyes and imagine yourself at Rifle, with the chains only a few agonizing moves away. Hang in there.