Comm. Jim Lovell was the Commander of Apollo 13. His responsibilities were to pilot the space craft during launch, keep his crew and spacecraft safe, pilot the lunar module and overall mission success.
Mr. Fred Haise was the Lunar Module Pilot. His responsibilities were to know and understand the systems of the lunar module and to help the Commander while he was piloting the lunar module.
Mr. Jack Swigert was the Command Module Pilot. His responsibilities were to know and understand the systems of the command service module, make course corrections during the flight, dock Apollo 13 with the lunar module and pilot the command module.
Dir. Gene Kranz was the NASA Flight Director. His responsibilities were to oversee all the operations of the Mission Control Center and ensure the safety of the astronauts.