A big mountain with both some of the easiet "climbing" in Africa, and, as Rheinhold Messner found out, some of the hardest.
Fly to Kilimanjaro International Airport and catch a taxi to Moshi or Arusha. Since guides are required on Kili, it's best (and basically your only option) to sign up for a guided trip up the peak. Once in Arusha or Moshi (or Marangu), you can easily find an outfitter that'll get you up the peak.
Just did the Lemosho to Western Breach route last week. The Western Breach is probably the 'hardest' summit route on Kilimanjaro. I didn't know what I was getting into climbing it--if you put a foot of snow on it, an exposed Grade III rock scramble at 18000 ft turns into a real mountaineering adventure, not just a hike. In 2006, 3 climbers were killed here due to rock fall, and they closed the route for a few years. The route is pretty steep and challenging. Definitely the way to go if you're a climber. If you want an experienced guide service to take you (which you must have to climb Kili), I highly recommend Destination Tanzania (www.detasa.com)--the guides know their stuff and they do a great job overall with the trip.