Advice for climbing Everest always recommends doing a lot of cardio workouts, and especially interval training. I've been doing this at least 3 times a week, either by running steps or on the hills around Chamonix. I've tried to vary this as much as possible to keep myself motivated.
My apartment in Chamonix is in a 7-storey building with a 115 step stairwell. I started my interval training using these stairs, running up and down the steps 10 times at least twice but sometimes 5 sets depending on how much other training I've done and how I feel. So, in total, I do between 2300 and 5750 steps in each session. The first time I tried I was walking up, running down, and it took 20 minutes. Then I started running up and walking down. Over the last 2 months my fitness has improved so I can run up and run down 10 times (1150 steps, up AND down) in less then 13 minutes. Then I have a 5 minute break and stretch, and do it again. Even when its -20 outside I can still comfortably keep up my training wearing the Rab Aeon Tee and shorts.
Once or twice a week I take the cable car to Aiguille du Midi at 3800m, and run up and down the steps outside the station. This was really hard the first time I tried, and the last few steps were real killers, I felt like I had a couple of elephants strapped to my thighs! I've acclimatised a lot since then and I can do intervals for 2 or 3 hrs now! This has no doubt helped speed up my interval training down in Chamonix too, as well as improved my tolerance to cold. Its usually -10 to -20 celcius plus windchill, and I'm warm enough in a Rab VR Lite Tour, Shadow Hoodie Wind Pro, Aeon t-shirt, Exodus Pants and Meco 165 thermals, Latok ice gauntlet gloves, beanie, and buff to keep the wind off my nose.
This is also where I've done some of my strength workouts, carrying a 20-30kg pack on the steps for an hour or two. Although I've stopped doing this on steps now, as my ankles and calf muscles hurt too much the next day. Doing it on an easy gradient hill seems to be much easier on the body.
The Aiguille du Midi station is the starting point for the famous Vallee Blanche off piste ski run, and the infamous ridge walk you have to negotiate to start it. I've done some interval training here too, wearing crampons running the steep ridge. Doing this in crampons is great for climbing technique. Sometimes I'm side stepping, sometimes front pointing, if I can do this at speed without tripping up, I shouldn't have a problem climbing on Everest!