For KIX, there are local trains every few minutes that run into Osaka. There is also the Deluxe Express "JR Haruka" that is a bit more expensive, has reserved seating and is a LOT more comfortable, particularly for large "gaijin." It runs every half hour from the station just across the second floor pedestrian walkway. I really like the Haruka and don't mind paying a bit more. It stops at Tennoji and Shin-Osaka stations in Osaka and Kyoto Station in Kyoto. 75 minutes to Kyoto.

http://www.kansai-airport.or.jp/engl...ess/jrwest.htm

For NGO, there is a dedicated local airport train that runs at least 3x per hour, more at peak times. It runs to/from Nagoya station and the airport station, also across a pedestrian walkway.

http://www.centrair.jp/en/access/ac-...ain/#timetable

For KIX and NGO, most train ticket sellers will speak some English, at least enough to sell you the tickets you need and direct you to the platforms. The tickets will have platform, time and car and seat numbers that you can read.

JR