The closest International Airport is Kilimanjaro IATA: JRO (http://www.kilimanjaroair...), and if coming from Europe, KLM Delta Air Lines (http://www.klm.com) has a daily non-stop flight from Amsterdam to JRO.
If you are coming from Nairobi, Kenya, you can fly with Kenya Airways (http://www.kenya-airways....), which works with Precision Air (http://www.precisionairtz.com/), and that would cost you about $400/person for a roundtrip ticket. Alternatively, you can schedule shuttle buses, which are at 8am and 2 pm daily, for about $25/person, one way, and its a 5-6hrs bus ride.
If coming from Dar es Salaam, you can fly into JRO for $320/person roundtrip; or take a 7-8hrs bus ride for $20/person one way to Arusha or Moshi.