You have to find Kilimanjaro climbing outfitter, get best price and make sure all services are inclusive while in Tanzania. Make sure you read all kilimanjaro climbing routes and choose which suits you best.
Then go to your Nearest Travel Agent, check flight tickets. Prices depend on which airline and connections. Usually KLM/Northwest Airlines do connect to Kilimanjaro International airport, JRO daily. Also Ethiopian Airline do, Swiss International Airline, British Airways/Precision Airways.
So choose which Airline to book and Kilimanjaro Airport is nearest to Kilimanjaro gate.
How to get VISA and immigration procedures.
If you have your passport, you can apply VISA at nearest Embassy of Tanzania. Also you can get VISA on arrival at Kilimanjaro Airport.
Now, you are ok to climb kilimanjaro in Tanzania. To read more about routes and make online booking peruse website http://www.kili-tanzanitesafaris.com
We traveled with Gap adventures to Kenya and Tanzania. After our tour ended we came home and some of the group did Kilimanjaro. You can check out the website. http://www.gadventures.com/trips/kilimanjaro/?ref=finder