From Kyoto city to Nara city, there are two train lines, JR and Kintetsu. There are criteria to choose which train are more suitable for you.
If you have a Janan rail pass, it is better for you to take a JR line. It takes 44min by a rapid train. (It takes 1hour by a normal one). But JR Nara station is a bit far from the popular attractions in Nara city.
If you take a rapid train, it takes 35min from Kyoto to Kintetsu Nara station. It costs 1,130yen. But if you take a normal train, it takes 52min. It costs 620yen. From Kintetsu Nara station, you can get to Nara park in 10min on foot.