there are a lot of different options for training to hit the mountain...
as said above, lift legs and the rest of the body as well...a balanced body is key for efficiency and capability...
squats...bar behind the head and resting level with the shoulders or just above the lower neck, slow descent provides a lot of negative resistance which strengthens in ways that simply exerting on the way back up will not...muscle should be working both up and down
leg extensions and leg curls...machine exercise but great for building strength in the hamstrings and the quads...i find single leg extensions and curls to be better than double leg (both legs at the same time) because the leg and its targeted muscles are more isolated...the idea of negative resistance can be applied here too
calf raise and seated claf raise...both work different areas of the calf, lower and upper and round out general leg strength
power lifts and cleans...great for developing explosive power, while not exactly what we may all be looking for (cleans are a little more racing oriented) i'm sure phys. ed would appreciate it...
lifting for the rest of the body...focus on the major areas...chest, tris, back, bis, shoulders and abs...
(chest)...bench press, dumbell press, incline and decline dumbell press, cable crossovers (where a cable is in each hand, starting arms out and drawing across the body to come together), flat and incline fly (dumbell in each hand, spreading the arms and then slowly bringing them together again)...all work core areas of the chest and are easy to incorporate into a workout
(tricep)...basic tricep pushdowns and pulldowns would be sufficient for general fitness and body balance, dips are good for the tris and are plenty when lifting bodyweight
(back)...lat pulldowns and rowing pulls on a cable machine are good for building and toning, increasing back strength, pullups with a wide grip (hands farther apart) are good for the upper back as well, back extensions on a 45 degree angled machine or stand are good for developing lower back strength (start with bodyweight and then increase with the addition of a medecine ball (heavy ball) or a weight itself
(biceps)...basic curls can be all you really need as long you focus on the idea of negative resistance and work just as hard letting the bar down as you do bringing it back up, fast and excessive reps with just a 45lb squat bar are good for toning and building endurance...hammer pull/lift (place weight on floor beside bench, stand at that side and place nearest knee and hand on bench while gripping and lifting with free arm) is good for general bicep strength also
(shoulders)...shoulder press with both the machine and dumbell is good for developing shoulder strength, dumbell lifts (dumbell in each hand, lifting up and out either in front of you or to the side with a straight and locked arms is awesome for the shoulders too
(abdominal)...a mix of high reps in crunches (various forms and crunch exercises, situps, leg lifts, etc) are good for toning and endurance and general strength, mixing up the routine with some decline situps and abwork can be really beneficial also
-calisthenics and plyometrics-
great for supplemental methods of training...the boxwork that was mentioned above is great for developing agility and jump strength, jumprope (leg strength and endurance), there is plenty more to incorporate if you want
key to general fitness and training for other physical activities, attributes to all areas and supplements lifting and plyo. work...regular mountain biking (typicalling XC but even downhill) and running (stay on dirt and grass, etc. because pavement and asphalt will fuck up your knees unless you've been running road for a long time), both are great for developing cardio, fitness levels and strengthening the legs
good luck with your work...