There are some options to travel between the destinations. Please consider the list below.
How to get from Fushimi-inari to Kiyomizu-dera temple?
If you have tight schedule, taxi might be the best answer. Especially if there are 4 of you.
The reason is that the closest train station to Kiyomizu-dera temple is about 25 mins away on foot, and there is no direct bus. So you need to change the transport or need to walk some kilometers.
Otherwise I recommend to take a train and then change to the bus for saving money, time and do less walking.
Option1: Use train and then bus to Kiyomizu-dera
There are Fushimi-Inari station and Inari station near Fushimi-Inari and you would like to catch a train from Inari station which is a JR station. Go to Tofuku-
Fee 140 yen for the train, if you hold Japan rail pass you can use it. 230 yen for the bus.
How much time The station is in front of Fushimi-Inari. 2 mins for train ride, and then about 15 mins bus. About 10 mins walk to the temple
Name of the stops JR Inari station to Tofuku-ji station, and then Tofuku-ji stop to Kiyomizu-michi stop or Gojo-zaka stop.
Which bus stop is better? Gojo-zaka vs Kiyomizu-michi.
There are not much difference in walking distance to the temple from these two stops. But Gojo-zaka stop is normally busier with other tourists and taxis so could be easier to walk from Kiyomizu-michi stop.
How to get to the temple from bus stopsFrom Gojo-Zaka From Kiyomizu-michi stop.
Option2: Use train to go to Kiyomizu-dera
You can travel from Fushimi-Inari Station (Keihan Main Line) to Kiyomizu-Gojo Station by single train. So it is simple public transport but there are about 25 mins walk from Kiyomizu-Gojo Station (The closest station to the temple.) to Kiyomizu-dera temple.
The train option is ideal if you have some spare time to sightseeing on the way from Kiyomizu-Gojo station but if you have busy schedule, you might want to go by buses or train and then bus, or simply use a taxi.
There are lots of things you can see between the station and Kiyomizu-dera temple. We did a walk from Gion-Shijo station, which is the next stop from Kiyomizu-Gojo station and saw as much as we could see around Kiyomizu-dera temple. (This is what we did.)
Fee 210 yen
How much time 5 mins walk to the station, 7 mins for train ride, and then 25 mins walk to the temple.
Name of the stops Fushimi-Inari station to Kiyomizu-gojo station by Keihan-main line.
How to get to the station from Fushimi-Inari?
How to get to the temple from Kiyomizu-Gojo station
Option3: Use buses to Kiyomizu-dera
Catching buses could be tricky in non familiar city but if you can use them well you could save lots of time and money. Kyoto city bus goes to most of major sightseeing places and the day pass is 600 yen. You can consider using that if you are planing to move around in one day.
Fee 460 yen
How much time 7 mins walk to the stop, about 10 mins ride on the first bus. 15 mins bus trip and then about 10 mins walk to the temple.
Name of the stops Inari-tansha stop to Tofukuji-michi stop. Tofukuji stop to Kiyomizu-michi stop or Gojo-zaka stop.
Simply use taxi to go to Kiyomizu-dera
Around Fushimi-Inari is crowded with shops and people and there are no taxi stops even at nearby stations. You can catch one driving around.
Fee about 1700 yen
How much time 15 mins or so