My physical training to climb Denali specifically was limited to roughly three weeks after Ironman Texas before leaving for Alaska (after a week to recover). Ironman covered the cardio and endurance needed for the climb (and the leg strength), I just needed to refamiliarize myself with carrying a heavy backpack. I did this by doing laps up and down "the hill of life," a roughly 200 foot vertical rocky trail near my office. It is the most vertical gain within a distance feasible for making two or three trips a week. I did about an hour of repeats per visit. I started with 40 pounds of old textbooks, and added 5 pounds each time I went back. When the pack was lighter, I managed to do 4 times down and up (starting from the top); when it got to 70 pounds, I only did 3 laps in the one hour. I found it fun carrying a heavy pack and passing people with either a light pack or nothing at all.
The technical training for this trip was done in February on Mt. Rainier, and since then just trying to practice some of the skills. I didn't find a way to practice crevasse rescue, but I did practice ascending a rope using prusiks and a mechanical ascender in the rock gym. Climbing Denali (at least by the standard route) doesn't require rock climbing, I just did some for fun.