Kenya can be accessed by all routes - road, waterways, rail and airways.
There are five major airports in Kenya - Jomo Kenyatta International Airport, Kisumu International Airport, Eldoret International Airport, Moi International Airport and Wilson Airport. The country is quite well-connected to various destinations. It is also important to note that USD 20 is levied on departures from Mombasa and Nairobi's international airports, as the tax.
Getting into Kenya by bus is also a good option. Buses frequently ply between Nairobi and Kampala, Nairobi and Arusha, Mombasa and Dar-es-Salaam and also Kisumu and Kampala.
There is a train route going to Tanzania, between Moshi and Voi. This service was re-inculcated into the country fairly recently, but now runs smoothly.
Kenya's highway network is pretty impressive. Its roads are also in good condition, making it convenient to get in by cab or car. You can drive in from the neighbouring countries via Moyale, which is a border town and even Uganda and Tanzania.
Getting in by waterways is possible as well. Mombasa-Zanzibar cruises are one option, followed by sailing in along Lake Victoria, i.e., Mwanza to Kisumu.