Do hill training. Many races at altitude involve uphills and downhills, so it's good to do a hill workout once a week to work on your hill running form.
Also see: "No-Hill" Hill Workouts
How to Run Hill Repeats
Benefits of Hill Running
Run by effort, not pace. You'll run slower at altitude, so use your effort, not speed, as your guide. Ease into your run -- you may even want to start out with a brisk walk. If you feel good after a couple of miles, increase your effort slightly and slowly build your intensity. During your training for your race at altitude, make sure you're familiar with your effort level for your race pace, so you know what effort level to dial in on race day. Some runners like to run with a heart rate monitor to keep their effort level in check.
Get to your race destination early. Your body can make adaptations to the lower air pressure at altitude by producing more oxygen-carrying red blood cells. But that process takes time. So, if you have the time and money, get to your race location at least two weeks early so you can sufficiently acclimate to the higher altitude.
Or, arrive right before the race. Of course, it's not always feasible to get to your race location a few weeks early. So the next best thing is to get there the day before your race. Huh? That's right, you'll actually feel your best during the first day or two at a higher altitude. After a few days at altitude, your body gets worn down from the stress of being at altitude and you could start suffering from side effects such as nausea, trouble sleeping, and fatigue. If you race right away, you can hopefully avoid all of those nasty side effects before and during your race.
Drink plenty of fluids. Once you reach your race destination, staying hydrated is an easy strategy to help your body more easily adjust to higher altitude. The air is much drier, so you'll need about twice the amount of water you'd need at sea level.
Also see: Running & Hydration