You can learn by doing and you can learn from someone who is better. This would require hiring a guide or following a more experienced climbing partner. In doing so the trick is not just to follow, but to ask questions and do things yourself. Imagine that next year you will have to repeat the climb all by yourself and learn with that mentality.
For MontBlanc you definitely need to be comfortable in crampons and have practice with self-arrest techniques up to the level when you do it automatically. The slopes are icy and the ridges are thin. You travel roped, even if you will not slip, your teammate might. Crevasse rescue is another thing to know. In my opinion the probability of slipping is higher than the probability of falling into crevasse, but knowing what to do will bring peace of mind.
There can’t really be too much of cardio training for the mountains. On the other hand, you do not need to be an Iron Man to go up MontBlanc. (But if you are – it definitely helps!). All depends on your speed ambition.
For the “Normal” routes you should be fairly comfortable if you run 10 K (6,2 miles) two – three times a week, preferably doing it under 1 hour. Of course, altitude may play tricks and some people acclimatize better than others.
Generally you may feel the effects of altitude already on 3600 – 3800m (11800 – 12 400 ft), almost everybody will feel some effects after 4400m (14400 ft). That’s why the last 400 elevation meters (1300 ft) may feel the most difficult, although not the most technical. But to know how your body reacts to altitude, you need to try. You cannot train for altitude, but knowing how your body responds is a great help.