The most comfortable option is Japan Rail (JR)’s limited express ‘Haruka’. At Kyoto Station the Haruka departs mainly from platform 30, though some early trains depart from platforms 6 and 7. It takes about 75min. From Kyoto, the first train is 5:45am and last train at 8:16pm. Here you can find train timetable: http://www.hyperdia.com/en/
You can buy tickets just outside the Shinkansen gates at Kyoto Station.
You can find more information here:
JR West website: https://www.westjr.co.jp/global/en/travel/shopping/access/train.html
Japan Travel website: https://en.japantravel.com/kyoto/best-way-to-and-from-kansai-airport-to-kyoto/404
Bus depart from the south side of Kyoto Station in front of Avanti store. I can help you make a reservation if you choose this option. The bus is very comfortable and costs about 2,550 yen and goes directly to Kansai Airport. In peak season it can get busy so it is best to book in advance.
The earliest departure from Kyoto Station is at 4.30 am reaching Kansai Airport’s Terminal 1 at 5.55 and Terminal 2 at 6:06.
The latest departure from Kyoto Station is at 21.40 reaching Kansai Airport’s Terminal 1 at 23.05.
Full timetables for the Limousine Bus service between Kyoto Station and Kansai Airport are available on the Kansai Airport website