Kyoto Arashiyama & Fushimi Inari back Osaka?

Hi, it is my 1st visit to Osaka and would like advice on how to get around to Kyoto. I am near Kintetsu Osaka Uehommachi train line. How do I travel to Kyoto Arashimaya and from there to Fushimi Inari Shrine ? How do I travel back from Kyoto ? Your advice, thank you.

Osaka Uehonmachi sta - Osaka subway Tanimachi kyu chome sta(walk, 5-7 mins)
Tanimachi kyu chome sta - Osaka subway Higashi Umeda sta(Tanimachi line, 10 mins)
Higashi Umeda sta to JR Osaka sta(walk, 5 mins)
JR Osaka sta to JR Kyoto sta(Kyoto line, 30 mins)
JR Kyoto sta - JR Saga Arashiyama sta(Sagano line, 12 mins)

JR Saga Arashiyama sta - JR Kyoto sta
JR Kyoto sta - JR Inari sta(Nara line)
JR Inari sta - Fushimi Inari(walk)

Check out Hyperdia.com. Just put in the two stations you need to start and end at and it will calculate the 5 best routes. If you don't know what stations, read the guides on this site (japan-guide) and the Access section for each major attraction will tell you which station to get off at.

Unfortunately the station you are staying at is a bit off the main lines to Kyoto, so expect multiple transfers to get to there.

I wouldn't go to Arashiyama from Osaka via Kyoto unless you have a railpass are are attempting to save money.

I would go from Umeda to Arashiyama via Hankyu lines. Then Arashiyama to Fushimi Inari on JR lines. The Fushimi Inari to back to Osaka on Keihan Lines.

You can use google maps and/or hyperdia to see these routes.