You can go either by Train, Land or Air.
With the Train, you only have the option, which is from Kampala, located in Uganda. The main railroad, Nairobi-Mombasa is connected with the line to Kisumu. The train is timetabled and so, you can crosscheck with the fares and the timetables.

The fastest and easiest way to penetrate Kenya is by air. The aircrafts usually land at Jomo Kenyatta International Airport.. Situated in Nairobi, Kenya Airways is the major Kenyan airline.

KLM (Amsterdam), Swiss/Cross Air (Zurich), British Airways (London) and SN (Brussels Airlines (Brussels), are some of the other airlines, which fly from Europe to Nairobi.
A connecting flight must be taken if from USA.

Other than Kenya Airways, there are International Airlines like Emirates, South African Airways, Egypt Air, El Al, Ethiopian Airlines, Air Malawi, Quantas and air Zimbabwe, that also fly to Nairobi.
Not many Germany Airlines fly direct from Europe to Moi International Airport in Mombasa. Only a few do, so from Munich (LTU) to Frankfurt (Condor), check with your home Flight schedules to Nairobi at Amadeus.

There is also a possibility of arriving by Land, but requires you to take some months off.
Nations to the West of Kenya, like Democratic Republic of Congo, in addition to nations to the North of Kenya like Sudan, Somalia and Ethiopia, face problems either chronically or sporadically. It therefore implies that the South route is the sole safe way to arrive by land in Kenya. The other relatively safe route is that from South Africa –Botswana-Zambia-Tanzania.
Bureaucracy could be the only problem since traditionally, a South African stamp in the Airport would make it quite hard to enter Kenya, but of late, such a restriction has been eased.