Californians overwhelmingly live at sea level, placing us at a distinct disadvantage when it comes to climbing mountains. The best and safest and most obvious way to acclimatize for high-altitude adventures—for example, climbing mount whitney—is to gradually adjust by spending several weeks living and training at progressively higher elevations.
If you can do that, great! Most people who live at sea level, however, will find it impractical to move to Mammoth, or Flagstaff, or Boulder. If you fall into that unfortunate group, take heart: there are strategies you can employ to improve your chances of success at altitude (or at least your comfort level), and there are certainly pitfalls you can and should avoid.
ELEVATE YOURSELF I.
It may not be feasible to permanently move to a mountain town, but you may have the flexibility to schedule trips such that they coincide with planned climbs. For example, I routinely spend a week or two every summer in Flagstaff, at 7000 feet. That's enough to confer a lot of acclimatization benefit, and over the years I've learned to immediately follow those Arizona trips with a Sierra climb back home.
Note that when you do return to sea level, accumulated acclimatization benefits degrade very rapidly. Sad but true: once you're back at home, within one to two weeks much if not most of the benefits you've earned will be gone. So time your trips as close together as possible to get the maximum benefit from this strategy.
ELEVATE YOURSELF II.
What if you can't spend even a week at higher elevation? There is some evidence that suggests spending as little as one day a month at altitude confers some benefit. So, for example, if you can put together one or two Mammoth trips per month over the winter, you may well be positioning yourself for spring mountaineering success.
I believe you ideally want to sleep in the sweet spot of 7000-8000 feet in elevation one or more nights per month to really get the best out of this approach. Note that sleeping higher is probably dangerous (for reasons we'll get to in just a moment). If you can't sleep high even one night per month, try to climb high once a month instead, for example doing Mount Baldy (10,000') via the ski hut trail.
Infrequent day trips like climbing Baldy may or may not provide a physiological acclimatization benefit, but they are profitable regardless, as they will add considerable conditioning benefit, plus they will force you to develop other altitude coping behaviors which will directly translate on future, higher-level objectives. I therefore consider such hikes mandatory preparation.
SLEEPING HIGH VS. SLEEPING LOW
Sleeping high is probably the single best acclimatization strategy of them all, but there's a catch: you must only do it when you are training! Sleep high on your actual climb, and you are setting yourself up for disaster. People repeatedly (and understandably) get this wrong, reasoning that if sleeping high confers benefits, they should do so whenever possible.
Would do you a set of squats right before a track event? Obviously not, and so too it is with sleeping high. When you spend a night at elevation, you are stressing your body. Spend a few days relaxing and recovering in your Mammoth condo, and you're soon good to go. Spend a night at Iceberg Lake, elevation 12,700', and then push for Whitney the following day, and you're daring AMS to crush you.
Is there some sort of Max-Min problem to be solved here? Yes, but it probably varies from person to person, and may even be inconsistent for the individual. Outside the context of training, I consider sleeping high universally dangerous for the non-acclimatized hiker or climber. If not acclimatized, I would rather sleep in Lone Pine than Whitney Portal the day before a hike.
There is disagreement on this subject in the wider climbing community. Some argue you can get net benefit rather than deficit by choosing just-the-right elevation to sleep at prior to your climb. But what's the magic number—and does it always hold true? The safe bet, it seems to me, is to avoid risking getting the formula wrong. Stay low except when training!
DELIBERATE HYPOXIA STRATEGIES
You may be interested to know that there are technological solutions available for altitude acclimatization. These include low-oxygen tents and oxygen-depriving breathers, which simulate but do not replicate the effects of high altitude on the body. The devices do seem to work, though long-term safety is unknown. I do not use them myself.
The opportunity has abruptly popped up and you want to give it a go. Is there anything you can do, with no acclimatization whatsoever, to cope with high-altitude climbing? Yes: technique. This would include overbreathing, pressure-breathing, and timing your breaths to your steps. The theory here is, for short periods of time, so long as you maintain your O2 saturation levels, you should be able to keep moving.
There are any number of ways this can all go horribly wrong, and I hesitate to detail these methods, much less endorse them. Worst case, you use such techniques to climb higher than you otherwise could, at which point you break down and your system goes into failure. While these techniques are wonderful supplements to a complete acclimatization strategy, they are a very poor substitute.
If you do choose to employ technique exclusively, be aware that you will be operating with very tight time constraints and very narrow safety margins. Even on hikes where your total time spent at altitude is mere hours, it is possible to get very sick very quickly, and we have new reason to believe permanent brain damage can occur at elevations that were previously considered safe.
Given the inherent conflict between my zip code and my love of tall mountains, I've spent a lot of time developing ways to cope with less-than-perfect acclimatization. It's still something I struggle with. There have been ibuprofen-laden up-all-nights spent taking deep breaths and praying for morning and a quick retreat. And there have been spectacular sea-to-summit successes as well.
Philosophically, I tilt toward conditioning myself on the hill rather than in the gym, so I tend to hike a smaller peak as preparation for hiking a bigger peak, and so on, leapfrogging up through benchmarks until there's no difference between my training hikes and my dream hikes. In training, I try to spend as much time up high as possible. When I'm hiking "for real", ironically, the reverse is true.