Take a walk off the beaten path. Authentic Cajun culture doesn't exactly litter the streets of the larger cities in Louisiana. If it's a true experience you seek, you're going to need to do a little driving away from the nearest airport or four-star hotel.
Take a tour. Most of the great adventures to be had in this part of the country are somewhat difficult to locate. Tour groups take the worry of getting lost out of your hands, while also providing interesting nuggets of information you may have never learned on your own.
Eat Cajun food. There is little that sums up Cajun culture like the rich, spicy and sometimes mysterious food the region has made famous.
Take a cooking class--even better than simply eating the food. There is something about preparing a Cajun feast that puts various aspects of the culture into place. Learn why red beans and rice are often served on Monday--while learning how to prepare this tourist favorite.
Enjoy the music. Louisiana is famous for much more than its jazz musicians. Take the time to find a zydeco musician and soak up the sound. If you can't find one that suits your mood, visit some of the music stores throughout Louisiana full of music that will enhance your experience.