They actually do run pretty regularly, and it'll say on the side of the train what kind it is: ひかり hikari、こだま kodama、and のぞみ nozomi. for the most part, shinkansen names will be in hiragana. They all stop on the same platforms; I actually boarded the right train at the wrong time and no one checked my ticket or anything. The frequency at which they stop varies depending on the station, obviously more frequent at the big stations and less frequent for the smaller ones, and many stations where the shinkansen doesn't stop at all (which is one of the reasons why it's so fast).
This site is a pretty good timetable thing, but unfortunately it's all in Japanese. If you or anyone you know understands the language, you should be set! http://ekikara.jp/
A transfer at Shin'osaka station will be necessary, since Tokaido Shinkansen (Tokyo to Shin'osaka) is operated by JR Central, while San'yo Shinkansen (Shin'osaka to Hakata) by JR West. Nozomi is the only choice to get to Hiroshima from Nagoya without transfer, except a couple of Hikari in the early morning.
JR Central airport bus might be a better choice than Meitetsu train for getting to Nagoya station from Centrair. Although it takes a half hour more ride, JR bus stops right in front of a Shinkansen ticket gate (approximately 15-minute walk to Shinkansen platforms from Meitetsu Nagoya station.)
Unfortunately JR Pass is not valid for the Centrair to Nagoya station bus route, it is going to be ¥1000 damage in cash. The voucher to be exchanged for a real pass at Nagoya station.
Thanks all! Someone has heard my prayers. New Hyperdia service working nicely. You can even choose Skinkansen expect Nozomi! What a great service now for Japan Rail Pass Travellers!