The Japan Railway System (JR) has various lines, which take you from the JR Kyoto Station to many different cities in Japan. Keihan Line is a useful transportation in East Kyoto (around Kiyomizu temple, Yasaka Shrine, and the Gion District). Keifuku Tram System is a convenient way to travel in Northeast Kyoto (around Shunkoin temple, Ryoanji temple, and Arashiyama).
The subway system in Kyoto has two lines: the Karasuma Line (north-south) and Tozai Line (east-west). The subway system is useful to go around the city center. After your visit Shunkoin temple and if you want to go to the city central, you take the JR Sagano Line to JR Nijo station. Then, you take the Tozai Line (subway) to Karasuma or Kawaramachi stations.
The bus network is the most useful way to reach many tourist attractions in Kyoto. The fee is a fixed fare of 220 yen. Also, a one day pass (500yen) is available at the JR Kyoto Station, bus terminals, and the front of each bus. You can use the bus network system unlimitely for one day.
In Kyoto, you can catch a cab anywhere, like New York or Boston. This may be the easiest way to go around Kyoto. If you reserve a cab for a whole day, it cost between 20'000 to 30'000 yen. After the midnight, the price gets more expensive (+10% of the daytime price).