1) start at http://www.japanrail.com which has details of the timetables and so on. There is a station at NRT with the Narita Express (NEX) running to Tokyo central station where you need to change to the Shinkansen (bullet train) to Kyoto. In my experience you can simply turn up and buy the tickets when you need to travel (perhaps get the return tickets when you arrive in Kyoto), and you probably don't need to get seat reservations - ask the ticket clerk when you buy. The nearest major airport to Kyoto is KIX (Osaka) but most (all?) domestic flights go to Tokyo Haneda, not Narita, which necessitates a long transfer. The train is the sensible option in both directions.

2) The Westin Miyako in Kyoto ( http://www.westinmiyako-kyoto.com/english/index_e.html )is very nice, and located on the edge of the city near the parks & temples. If you like walking around cities then you will find that Kyoto is sufficiently compact to be able to see most of it this way. The Westin also has a free regular minibus service down to the train station up until 6pm.