Climbing a 14er efficiently requires a certain level of fitness. The difficulty you'll experience attempting to reach the summit varies tremendously based on your age, physical condition, and other medical factors. What I'd like to accomplish is defining some training methods you can utilize to improve your ability to climb 14ers efficiently. Obviously getting out to the mountains to hike uphill at altitude is the best training, but on the weekdays when you have to work, a quick gym or home workout may be easier to fit into your busy schedule.
1) Weight Loss. The elephant in the room. If you are like most Americans, you could benefit from reducing the amount of body fat your are carrying around. Each extra lb of fat you are carrying diminishes your ability to climb uphill, and puts additional wear on your knees. Just imagine the difference between climbing stairs unemcumbered, or while wearing a 20 lb backpack. If you are unsure of your bodyfat percentage, you should consult your doctor. You can also reference the BMI chart, but keep in mind, this chart is an estimation only and may not be accurate for some individuals.
2) Cardio. This is obvious, but cardio is a huge factor in climbing 14ers. You will be spending 4-10 hours hiking, so the ability to maintain a manageable heart rate while climbing at altitude is important. Being able to recover quickly is also important.
Running outside is great exercise, it's free, and a lot of people can do it. Ideally you'd want to be able to run 3+ miles at a steady pace without stopping to rest or walk. Running improves cardiovascular and provides a similar light impact workout to hiking.
Running or walking stairs is another good exercise. You could substitute a stairmaster or stair stepper if you have access to that. In addition to improving cardio, this does work on some muscular strength.
Lastly, HIIT workouts have been getting a lot of attention lately because of their big benefits and short time commitment. High Intensity Interval Training involves intervals of intense activity followed by a more moderate activity. Common intervals include 1 minute of high-intensity exercise followed by 1 minute of low-intensity exercise. This cycle repeats 3-10 times. A common interval method involves walking and running on a treadmill.
3) Body weight exercises. These can be very helpful to increase your strength, which becomes more important as you get into steeper climbs like class 2 and class 3. These can include bodyweight squats, lunges, walking lunges, and box jumps (or box steps). This could also include pull-ups, push-ups, and dips. Planking, mountain climbers, and flutter kicks all work on your abdominals and core, which is good for balance and stability. The best part about bodyweight exercises is that they are free to do because they require minimal or no equipment.
You can also do things like lunges, squats, and pull-ups with a weighted pack on to simulate hiking just a little better.
4) Free weights. While not strictly something you would do for hiking fitness, these exercises are great for core strength, muscle mass, metabolism, and strength. You will not automatically get "bulky" when you lift weights either. Suggested exercises that help with climbing 14ers would include: Deadlifts, squats, lat pull-downs, decline bench press, weighted dips, and anything that would help with legs, core, or grip strength.
I've also become a big fan of Back Squats (weighted squats) for hiking. Back Squats develop nearly every single muscle in your legs, your glutes, and your core. If you go down this route, doing many reps of roughly your bodyweight is a good way to train up for climing mountains. It will also add strength and stability to your knees, and increase your metabolism.
In general, weighted exercises should come before cardio if doing both activities on the same day. Workouts should be limited to 60 minutes or less, but be at least 10 minutes for HIIT or 30 minutes for steady state cardio.
Warm-up: 3 sets of walking lunges, 1 minute each.
8 minutes of jogging at an easy pace
HIIT: 60 seconds of running (8-10+ mph), 60 seconds of walking (3.5-4 mph) x (5-10 intervals)
Cool-down: 5 minutes of walking at a moderate pace.
If you have access to a large staircase, you can run up the stairs and then walk down, repeating several times.
Warm-up: 3 sets of 40 bodyweight squats
5-8 minutes on the exercise bike, low to moderate effort
20 minutes on the stairmaster, fast enough to get your HR up really high (consult a HR chart if you don't know where you should be)
5-10 minutes of cooldown walking or riding exercise bike