You can take the Haruka Express directly to Kyoto. It will take about 75 minutes and cost you about 3500 yen.

You can take a combination of trains that will first take you into Osaka, where you can transfer to a train or subway to Kyoto. It can take you up to 2 hours easily.

You can aslo take a bus or shuttle to Kyoto. Price and departure based on which service you choose. The bus is the easiest because some of the others require advance booking.

Check out this page for general information:

http://www.japan-guide.com/e/e2033.html

You can also go to the Kansai Internatinal Website. Check out the page below. When you do you will notice the "Hyperdia-timetable link".

http://www.kansai-airport.or.jp/en/access/train/index.h...

Select it. Enter Kansai for the start point and Kyoto for Destination. Select a time. You will get a list routes, time and cost.

JR West Pass(2000yen) pays off for just oneway trip to JR Kyoto station by direct train.

If you do not have a Rail Pass then I highly recommend you take the bus. You can store your bags underneath and just wait until the bus drivers stops in Kyoto. From there you can take a taxi to your Japanese inn.