There's busses leaving infront of the airport to other cities- one to Kyoto as well.
You can buy the ticket from a ticket machine (close to the busses), and if I remember ir right, the ticket was something like 3000 yen. (approx 20 euros?)
It stops at various places, but you can stay off for example at the Kyoto Station, and continue to your hotel from there by public transport or by taxi.