Acclimatisation is the whole subject on Kilimanjaro. Understand it and the rest of the planning makes sense on its own.
What your body is doing
Within hours of going up, you breathe faster and deeper, and your heart rate rises. Over days, your kidneys adjust your blood chemistry and your body starts making more red blood cells. That second part is the real adaptation and it needs time rather than effort. There is nothing you can do to hurry it, which is why days on the mountain buy summits.
Climb high, sleep low
The principle behind every good itinerary. What stresses your body is the height you sleep at, not the highest point you touch. So a good day walks up to a high point, stays a while, then comes back down a few hundred metres to camp. You get the stimulus without the night at the altitude. This is why your guide takes you on a short uphill walk in the afternoon when all you want to do is lie down, and why the Machame route climbs to the Lava Tower at around 4,600 metres and then drops to Barranco at 3,900 to sleep.
How much height per night
The general mountaineering guidance is to raise your sleeping altitude by no more than 300 to 500 metres a night once you're above 3,000, with a rest day every so often. Kilimanjaro itineraries break that guidance routinely, because the mountain is shaped the way it is and the camps are where they are. The longer routes break it least, and that's the entire difference between a five-day climb and an eight-day one.
Why slower is faster
Pole pole. Walking slowly keeps your effort below the point where you're gasping, which keeps your oxygen saturation up, which leaves more of your body's capacity free for adapting. People who race the first two days are over-represented among those who go home early. If you can't hold a conversation while walking uphill, you're going too fast.
Drinking, and why there's so much of it
You lose a lot of water just breathing dry air, and dehydration thickens your blood and mimics altitude symptoms. Three to four litres a day. Clear urine is the crude but effective test, and your guide will ask.
Does being fit help?
It helps you enjoy the walking and recover between days. It does not protect you from altitude, and that surprises people every week. Age, sex and fitness are all poor predictors. Previous experience at altitude is the only halfway useful one, and even that isn't a guarantee.
What doesn't work
Arriving a few days early in Moshi, which sits too low to do much. Pushing through a headache. Alcohol. Sleeping pills, which suppress breathing at exactly the wrong time. And going faster to get it over with.