Sendai to Fukushima
Buy your ticket at a JR Ticket Office, which you can recognise from the word みどりの窓口(midori no mado guchi) or from this logo:
To check the train times in advance, and for more information on JR stations (including station maps and the layout of shinkansens, please check here)
To go to Koriyama or Fukushima, just get off the shinkansen at that station.
To go to Aizu Wakamatsu, you need to change trains at Koriyama station, and take the Ban-Etsu West Line from Koriyama to Aizu Wakamatsu station.