Phil,

Here goes.  The heart of Cajun cooking is making a roux.  There is a really good authentic cajun cookbook called "First You Make A Roux" and this truly is how cajun cooking goes.

The tricky part is timing.  It's important to have all your ingredients ready to go before you start so this would be the secret. 

Also, make sure you have about half an hour with no distraction.  If you answer the phone, your roux burns.  If you walk away to get a drink, your roux burns.  If you sneeze and stop to blow your nose .... you get the idea.

Step 1.  Chop up one large yellow onion and have ready
Step 2.  One whole cut up chicken - seasoned on both sides & ready
(An authentic Cajun seasoning is called Tony Cacherire's and is in a green container.  If not available salt, pepper, red cayenne pepper will suffice)
Step 3.  Put out a container holding 3 cups of water.
Step 4.  Use a heavy large pot (a black iron dutch oven is best)
Step 5.  Over moderate heat put in 1/2 cup of vegetable oil and 1/2 cup all purpose flour
Step 6. Stir constantly getting as smooth a consistency as you can.
Step 7. Keep stirring.  You will find that it is sticking to the bottom of the pot as fast as you can scrape it off.  Be consistent, stirring constantly back in forth unsticking the bottom.  It may take 20 minutes or more.
Step 8.  When the roux is medium to dark brown (between the color of a regular caramel and a dark caramel - remember those little square ones?)
it is ready. 
Step 9.  Put in the onions all at once and STAND BACK!!  Just like a science experiment you will have a whoosh of heat and steam for just a second.
Step 10.  Immediately start stirring again.  (Thought you were through stirring didn't you?)
Step 11  After another 15 minutes or more of CONSTANT STIRRING your onions will be getting clear and soft.  (The roux won't get much darker once you add the onions)
Step 12  When the onions are clear slowly add in all three cups of water and all of the chicken pieces.  Bring to a boil and then lower to simmer for at least one hour, stirring occassionally - maybe three times during the hour.
Step 13.  Cook some rice.  I usually set the timer for an hour and when it goes off I put my rice on which takes about 15 minutes (the power of microwave) so I just let the chicken keep cooking to get a little more tender.
Step 14.  Serve.  We usually have white rice with gravy on top and sweet peas are the usual vegetable as the sweet taste contrasts well.  (I mix mine together =) but that's just me.

A little Tony's on the table for those who like it a little spicy and you're ready to go.  Great comfort food.

It looks like a lot of trouble, but it's just during the roux stage that it is hard.  After that you can forget about it until it is cooked.  Some people get the roux right the first time, for some people it takes years, and other never get it right.

But remember, first you make a roux ....  After that it's gumbo, fricasse', crawfish stew, crawfish ettouffe', all starting with a roux.  My mother in law even made a small roux for her spaghetti. 

Have fun.  Let me know how it comes out.