Shinkansen bullet train from Kyoto to Tokyo?

There's frequent train service between the cities. Purchase your ticket at the time of travel.

There is no need to book in advance, unless you're traveling in the peak season. www.hyperdia.com for schedules and fares throughout Japan.

There is a discount ticket you can get on the Kodama trains, but it requires advance purchase, other wise purchase on the day - the ticket machines are easy to use (they have several language options), and faster than queuing for the normal ticket counter.The Nozomi is the fastest train between the two cities. If you have any seating requirements, like window/aisle, or sitting together with your other travelling members, reserving in advance is recommended. (You can reserve 3 days in advance, at the JR ticket machine)

You can know more about the JR pass in this video:

hello 

I'm traveling to japan in March. This is our first time to Japan. We are on a budget limit.  We are in group of 7 people. I'm flying down from tokyo narita.  but my first 4 days going to be in Kyoto, then osaka (4 days)  and 8 days in tokyo. What is the best way for transportation? I'm fly in from tokyo around 4pm. Also I see this JR west Kansai area pass in govoyagin. It cost $20.06 person. How does this pass work? Can I use this pass on bus, or trains that take me to Gion, Fushimi Inari shrine temple, kiyomizu dera temple, Nara, ects... Thank you. 

5% OFF JR-West Kansai Area Pass 1/2/3/4 Day Bus & Rail Pass