One thing that also really helps is to listen to another or several other versions of the song. Another singer's articulation, or a more resonant voice, or a woman's voice instead of a man's voice, etc. can suddenly make a whole passage sound much clearer.
Well, that's what I have always noticed for English songs (an American version, for instance, was always clearer to my ears than an English version, J. Cash was always clearer than the old versions of the songs he was covering, etc.). Then you can go back to the original and you will recognize the words.
I got it from Ann's book, repeated listenings to the CD, and a little help from a Cajun teacher at a fiddle camp. Initially, it took me several months to memorize. That was 10 years ago, and it's still a work in progress. Even now I can hear the song and realize, "OK, I've been pronouncing such-and-such word wrong." I highly recommend memorizing not only the words but their meanings as well. Get a Cajun dictionary and look up every word you don't know. It's a lot of homework, but it will help you remember this song better and make learning the next song that much easier.
Two things will help you learn the lyrics. Ann Savoy's book and the Amazing Slow Downer. This is available for PC and Mac and will let you slow down the speed of a song all the way down to 20% and it will still maintain proper pitch. You can slow down your tune and follow along with the book. I swear by the Slow Downer and recommend it to anyone who is trying to learn Cajun music.