Watch the Apollo 13 movie. It's surprisingly accurate with a few notable exceptions, to add some drama, and some stuff is simplified for the screen and for time reasons. Much of the actual mission is portrayed exactly as it happened, down to much of the dialogue being pulled directly from the original air to ground tapes.
Tom Hanks got his wish to be an astronaut. :-)
Also, as /u/Dawpr suggested, Jim Lovell also wrote a book, upon which the movie is based. It has some details that the movie had to leave out for time. Here it is on Amazon, with no affiliate link or BS.
Apollo 13 is an engrossing account of the mission, a great read. http://www.amazon.com/Apollo-13-Jeffrey-Kluger/dp/0618619585