Your chosen trip intensity level should be appropriate for your known physical abilities. But your experience will be more enjoyable and more comfortable if you improve your fitness beforehand.
Training should prepare you most for the vertical change, off-trail travel, and pack weight. I would not focus as much on training for mileage — it’ll happen naturally in the process of training for the other factors.
If your trip will be at high altitudes (e.g. 8,000 to 12,000 feet above sea level) you may want to take some additional precautionary measures.
Vertical gain and loss
Find vertical near where you live (e.g. mountains, hills, stadium stairs, parking garages, etc.) and train there regularly.
Do NOT believe that good overall fitness can substitute for vertical-specific training. Each year, some clients struggle with the vertical more than they expected because they didn’t incorporate it into their training.
If you have gym access, do one-legged squats (high reps, low weight), plus sessions on the Stairmaster and/or treadmill with the incline at its max.
Off-trail hiking requires better balance and more power, and a Zen-like attitude — don’t get frustrated, because it is what it is.
Start hiking off-trail. You won’t go as far or as fast, but you’ll still get a comparable workout, and you’ll start strengthening all of those balancing muscles. If you are not comfortable yet going too far away from a trail, don’t, but still get off-trail for short sections.
Instead of hiking on “trails” made of concrete or pea gravel, find nasty, technical trails that are full of rocks, roots, blowdowns, or soft sand (especially if you are joining us in Utah). Again, you won’t move as fast, but your workout will be the same.
At the start of your trip, you should expect your pack to weight 15-20 pounds for a 3-day trip, about 20 pounds for a 5-day trip, and 20-25 pounds for a 7-day trip. Your upper body needs to be trained to support this weight, and your legs need to develop the strength to move it.
Do some of your training with a fully loaded pack, even if that means adding excessive water or food to your load, or even putting rocks or bricks into your pack.
Do shorter efforts with an even heavier pack. For example, one client told me he has been doing repeats with a 40-lb pack on a small nearby hill with 150 vertical feet. Don’t go overboard here, however — it’s easier to tweak a knee or ankle when carrying a lot of weight. Build up to it.
If you have not been at altitude before, or have not been at altitude in a while, you may experience acute mountain sickness, the common symptoms of which are headache, light-headedness, nausea, and loss of appetite. Efforts to train for elevation will help you avoid, reduce, or quickly get through these symptoms.
If you have access to high elevations (sorry, East Coasters), try to get up a few times before the trip.
If your travel schedule allows, stay at altitude for two nights before the trip. If you live at sea level, one night is the minimum.
And, finally, increase your cardiovascular fitness with high exertion activities like running, rowing, and cycling.
If you have known issues with altitude, you may want to consult with your doctor about precautionary medications like Diamox.