If you're in good shape, exercise regularly, hike and jog and stuff like that, you should be able to do it. I think a healthy, fit 65-year-old should be able to make it to the top. At the time I was 34, not very athletic, and I only made it to the third hut (at 4740 meters, still higher than California's Mt. Whitney, the highest point in the U.S. minus Alaska). Even though the mountain is 5895 meters high, it is not a technical climb. You don't have to know how to use climbing ropes, or have any mountain climbing experience. However, the altitude gets to some people, even fit young people, and in my experience there is no way to tell who it's going to hit. Maybe 1 in 10 have severe reactions to altitudes above 4000 meters or so. Taking it slower and acclimatizing usually isn't an option, because you're on a schedule, and have to camp at the right hut each night. My climb was 5 days round trip, and this is what people do, but there are other itineraries which take an extra day or two or three. If I were doing it now I think I'd look into one of them.
The starting point for the climb is 1860 meters, and the round trip is about 60K in 5 days.
I like Africa On A Shoestring. Since it attempts to cover all of Africa, you might want to get Lonely Planet's East Africa instead.
One of the things I like to do when travelling is to read books that have something to do with where I am. On Mt. Kilimanjaro, I read "The Snows of Kilimanjaro" by Ernest Hemmingway. It's just one of several short stories in the collection, and I think a good introduction to Hemmingway if you haven't read him before. I also read Hemmingway's "The Green Hills of Africa" while there. These books are always called bloody and violent; but I'm what you'd call a bunny-hugging environmentalist, and they didn't bother me. Great stuff. You can read them even if you don't go to Africa.
There are other routes, where you stay in tents, but the most common one, the one I went on, is like this:
Day one: start at the park entrance at 1860 meters, and walk to Mandara Hut, 2725 meters. This is an easy walk up a fairly gentle climb. You're in lush forest most of the way. The porters carry your sleeping bag and food and whatever else you want them too. You carry just your lunch, water, a jacket, and camera if you want. Our group had a guide, but I never saw him. It's impossible to get lost: there's only one path, and everyone is going the same place. You see other people, from France, Germany, Australia, all over, coming down the mountain. Mandara Hut is right at the edge of the rainforest, where it changes to grassland. It's really a large common lodge where you cook and eat, and a collection of several small cabins, each sleeping 4 people. My stuff that the porters carried was in my cabin when I got there. There are pit toilets. Water is available, but no showers. The porters and guides cooked our food, and cleaned up afterwards.
Day two: Hike to Horombo Hut, 3708 meters. Quite a climb; not steep, but relentless. You pass above the clouds and start to get views of the plains below. The terrain is rolling grassland, but the trail just goes up, up, up. Accommodations are similar to the first night's.
Day three: Hike to Kibo Hut, 4740 meters. I had carried my camera the first two days, but not this one; it got too heavy. The grass thins out, and you enter a Martian-like landscape, with nothing growing except some lichen. You really notice the altitude. Kibo Hut isn't like the other two, it's just one building, with several rooms and bunk beds. Pit toilet outside. It snowed when I was there.
Day four: Get up at midnight, after just a couple of hours sleep. Put on your long underwear and extra clothes. Eat breakfast, and hit the trail by 1AM. Climb to Gilman's Point (5685 meters) in the dark, and Uhuru Peak (5895 meters) hopefully in time to see the dawn. At this point I have to admit that I didn't make it much past Kibo Hut. My joints ached. The guides (I'm told) are a real help now, in the snow and in the dark. You walk down past Kibo all the way to the second night's hut, Horombo.
Day five: Walk down, past the first night's hut, and all the way out. My group was camping on the grounds of a hotel not too far below the park entrance. Most tours will take you off to Moshe or Nairobi in a bus.
I don't think it matters much, since Mt. Kilimanjaro is so close to the Equator. Days and nights are always the same length, and they don't have summers or winters. However, they have two wet seasons (the "short rains" in October and November, and the "long rains" in March, April, and May).
But if you're going to be combining a Mt. Kilimanjaro climb with wildlife viewing in Tanzania or Kenya, like most people, you may wish to avoid the rainy seasons. The reason is that when it is dry, it is easy to find the big game animals -- they're at the waterholes. When its rainy, they could be anywhere. Also, most of the roads in the game parks (and a lot of them elsewhere) are dirt, and get muddy in the rainy seasons.
That, at least, is the conventional wisdom. I was in East Africa from February until May, including visits to Ngorongoro Crater and the Serengeti in February, when it was dry, and again in April, when it was wet, and I saw about the same numbers of animals both times. And muddy roads just add to the adventure.
My trans-Africa trip was with Guerba, and booked through The Adventure Center in Emeryville California. They are the U.S. agents for a number of companies operating in Africa, and I recommend them. They will also arrange flights from the U.S. to Africa. Guerba, and most other companies operating tours in Africa, are British. If you're in the U.K., you can deal directly with them. In other countries there are other agents.
You can book a trip while you're in Africa, but I, for one, would rather have this all arranged before I left. There are scam artists in Nairobi, like anywhere else. You can also just show up at the mountain, but won't save much money this way, because you're still going to have to pay for your time in the park, for the huts, and for porters and guides.
In 1990 I paid $80 in park fees, and about $100 for my share of porter fees and food. This was for 5 days, 4 nights on the mountain. With some other miscellaneous expenses it was about $200, not counting transportation to and from the mountain.
I looked up current fees (as of 1999): $25 per person per day park fee, plus $50 per person per night hut rental, plus unspecified (but required) porter and guide fees. It probably comes to about $500 minimum, not counting transportation to and from the mountain. All money must be paid in hard currency (US$ or UKŁ; maybe they take Euros now.)
At the time I'm writing this (17 November 2000) I see that the price of the 7 day Guerba climb, including transportation to and from Nairobi, is $1350 US. With the transportation and a couple of nights in hotels, I doubt that Guerba is making a huge profit.
The Tanzanian government is using Mt. Kilimanjaro (as well as the Serengeti and other major game parks, which cost $100 per person per day) to generate foreign exchange. I don't begrudge them a bit for this. Tanzania is very poor by US or European standards (though a lot better off than much of Africa) and if they have a way to make money off of nature and wildlife, more power to them I say. It is an incentive to keep the wild areas wild. Besides the park entrance fee and hut fees, they require you to hire local guides and porters. This is another way of transferring a bit of wealth from rich tourists to poor Africans.