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.