Pretty easy...
Boil some chicken in chicken stock with your favorite cajun seasoning and when done shred and set aside.
I pan sear the andouille and set aside. Not everyone pan sears it
Cut up the celery, bell pepper and onion set aside
Make the roux (1 1/4 cup of flour and 1 cup of oil is what I use). Stir over medium low heat until it reaches a dark color ~45min
Add the trinity when roux is done and sweat them out ~5min
Add some of the chicken stock from step one to cool it down and stop the roux from cooking
Add the chicken and andouille as well as more stock
Throw in more of your favorite cajun seasoning and a few bay leaves and simmer
I usually let it simmer for at least an hour before serving, but the longer you can the better it will be.
I can't remember who said it on TOS(maybe Brisket?), but it went something like this
Step 1. Make the roux
Step 2. Put whatever the fuck you want in it after that.