I have mentioned this a few times, but the cheapest way to get to Tanzania and climb Kilimanjaro is via Nairobi, and typically through Kenya Airways, which has cheap flights from London. If you are coming from the US, find the cheapest flight to London, and then check with Kenya Airways. Also, check out BootsnAll Travel Networks air ticket deals to Kenya. There is some good rates and it uses all the major airfare engines.
If you want to pay a bit more, but have an extra day, you should fly into Kilimanjaro International Airport. BootsnAll also lists airline tickets deals in Tanzania and elsewhere in Africa.