Apollo 13 was manned by James Lovell, who was the commander, and who has flown on a few previous missions during the Gemini and Apollo programs. John Swigert was the command module pilot, though he was a member of the back up crew, he replaced Ken Mattingly who was thought to have been exposed to rubella. The third crewman was Fred Haise, and he piloted the lunar module.
The crew was asked to perform a cryo stir, which stirs the oxygen tanks. Wires that were damaged caught fire during the stir which caused a pressure increase and boom, the tank blew. This blew both oxygen tanks, so they had no oxygen basically. They lost power due to the explosion, well lost power in the Command Module. They also had to build extra filters to filter out the Carbon Dioxide they were exhailing, they did so by using parts in the spaceship. They had to make a course correction in order to get back to Earth, and I believe they had to use the moon to help propel them towards the Earth by slingshotting around it. When they got to Earth they had to use the thrusters on the Lunar Module to manuever since the Command Module was dead since they were saving what battery power was left. Once they began re-entry they had the batteries activated and landed in the ocean.
