Zambia’s main international airport is in Lusaka, and there are smaller ones at Livingstone – best for Victoria Falls - and Mfuwe – easiest for South Luangwa National Park.
Arriving by train is far cheaper and an excellent way to see the beautiful countryside, but it obviously requires a far greater time commitment. TAZARA line trains run between Zambia, and Tanzania twice a week.
Although Zambia is landlocked, It borders on Lake Tanganyika, and ferries operate across the water a few times a week. The M/V Liemba will carry you across the lake for a reasonable price, its not a quick option, although the charm of travelling in this way more than makes up for that.
There are numerous route to enter by road. Crossing the border by car incurs an extra tax, but gives you the option of flexibility, whilst catching an international bus into Zambia allows you to relax during the trip, but slows you down significantly while everyone is processed through immigration at the border.