Narita to Iwakuni

I want to travel from Narita airport to Iwakuni. What is the best procedure? I would like to take the Nozomi but cannot seem to find an actual fare

If you want to take the nozomi, you should first take the Narita Express from the airport to Tokyo (Tokyo or Shinagawa Station) and then a nozomi to Hiroshima. From Hiroshima, you can take either a kodama shinkansen or local train to nearby Iwakuni:
http://www.japan-guide.com/e/e6176.html

An alternative approach would be by air from Narita Airport to Hiroshima Airport. There is one direct flight from Narita per day.

Do I need to get the tickets here in the U.S? and how do I find out how much the train is and how long the trip will take. Do I need to change trains? If so, how many times before Hiroshima? The websites I looked at were really confusing!

Do I need to get the tickets here in the U.S?

No, you can buy them after arriving in Japan.

and how do I find out how much the train is and how long the trip will take.

By train it takes about 6-7 hours and costs around 21,000 yen one way.

Do I need to change trains? If so, how many times before Hiroshima?

Yes, twice. Once at Tokyo or Shinagawa Station. And a second time in Hiroshima. If you use a Japan Rail Pass, a third transfer is necessary at Shin-Osaka Station.

What is the time and money difference between the Nozomi and the JR?

Nozomi trains are also JR train! You just cannot use them with the Japan Rail Pass. But you can use hikari trains instead, which take about 30-60 minutes longer.

Thanks!

http://www.hyperdia.com/cgi-english/hyperWeb.cgi

you can use this website to get detailed information. Type in Narita Airport and Iwakuni and then set your conditions (maybe uncheck the airline box)

Your options include:
- Hiroshima Sta. to ShinIwakuni Sta., via Shinkansen Kodama
- Hiroshima Sta. to Iwakuni Sta., via San'yo (Main) Line
There is no direct JR route between ShinIwakuni Sta. and Iwakuni Sta.
For details, see the japan-guide.com page linked to by Uji.

Shinagawa Sta. sounds better for changing trains from a Narita Express to a Shinkansen. (The two tracks are located near.)
If you change trains at Tokyo Sta., the required time is estimated at 25 minutes or more, because you have to go upstairs from the fifth basement and advance along a long pathway.

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Thanks. For all that I think I am going to pay the extra and fly directly into Hiroshima. By the time all is done I would only be saving myself about $100. Not enough to schlep my suitcase through the train station.

Note that there is only one direct flight from Narita to Hiroshima per day. Currently it leaves at 17:25. There are a lot more flights leaving from Tokyo's second airport, Haneda Airport, but that airport is a 90 minute bus ride away from Narita.