Limited express train "Haruka" served by JR goes directly from KIX station to Kyoto station.
You'll arrive at the international arrival of the first floor of KIX building. There is an overbridge from the second floor of the airport building to the airport station, so you'll use elevator or escalator to go up to the second floor.
After going across the overbridge, there is a joint train station of JR line and Nankai line. Nankai line only goes to the southern part of the downtown Osaka (Namba), so do not use that line.
At manned ticket counter of JR, you'll say "Kyoto, Haruka". (Or you may be brave enough to try automatic vending machine.) All Haruka seats need reservation but the tickets with reservation would be easily bought at the KIX station. The fair is 1,830 Yen basic fair plus 1,660 Yen limited express charge (total 3,490 Yen). It leaves almost every 30 min. from 6AM to 10PM. It takes about 75 min.
At Kyoto station (final destination of Haruka), you follow the sign to Subway and get to the subway station. There is only one subway line, called Karasuma Line, going through Kyoto station. At the subway station, you buy a 260 Yen ticket to go to "Kokusaikaikan" (Japanese translation of International Conference Hall). Kokusaikaikan station is the northern terminal of Karasuma Line.
You would have to use automatic vending machine to get subway ticket at almost all subway stations, but it is easy. At first, you check the fair by signboard above the vending machines. Then, you put enough coins or a bill to the machine, and push a button with listed fair. The ticket and changes will come out.
The subway to Kokusaikaikan comes every 5-10 min. The final destination, Kokusaikaikan is the tenth station from Kyoto.
At Kokusaikaikan station, you would easily find the direction of Conference Hall and Prince Hotel. You will follow the sign and go up to the ground where you'll easily find signboard and recognize Conference Hall and Prince Hotel. Both Conference Hall and Prince Hotel are about 5 min. walk.
At Narita Airport Station, there is a joint train terminal of JR line and Keisei Line. At ticket counter for JR line, you would say "Kyoto by Narita Express and Hikari with reservation". You'll get three tickets, basic fair ticket to Kyoto, limited express charge for Narita Express, and limited express charge for Hikari (Hikari is a type of limited express of Tokaido Shinkansen line).
You first ride Narita Express to go to Tokyo Station. One or two Narita Expresses leaves every hour at Narita Airport Station from 8AM to 9PM, and it takes about one hour to go to Tokyo Station. Tokyo Station is NOT the final destination of Narita Express. (Shinjuku, Yokohama, etc.)
At Tokyo Station, you move to Tokaido Shinkansen platform, and take the Hikari train specified by the ticket. In case you missed the assigned Hikari, you can use non-reserved seats of later Hikari's. Hikari leaves almost every 10-15 minutes from 6AM to 8PM. If you would like to try more speed, you would use Nozomi, instead of Hikari. Hikari takes 2 hours 45 minutes but Nozomi takes 2 hours 15 minutes. Nozomi leaves Tokyo twice an hour. Kyoto is the 2nd, or 3rd (or more) station from Tokyo, depending on trains.
The fair is 9,030 Yen basic fair plus 1,660 Yen Narita Express limited express charge and 5,240 Yen Hikari limited express charge, totally 15,930 Yen (there may be a small difference based on date to ride). If you want use Nozomi, you need extra 970 Yen.
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