NKFF does not subscribe to a particular method of fly casting. After all, fly fishing is an art and part of what you lay on the canvas is the cast. However, there are certain basic concepts of the fly cast that must be mastered before you can effectively add your own creativity. We teach basic fly casting as a part of our introduction to fly fishing class. In particular the beginning fly fishing class covers the documents, Learn To Fly Cast by Joe Fly-rod and Fly Casting Basics.
"After my brother and I became good fishermen, we realized that our father was not a great fly caster, but he was accurate and stylish and wore a glove on his casting hand. As he buttoned his glove in preparation to giving us a lesson, he would say, "It is an art that is performed on a four-count rhythm between ten and two o'clock.""
~Norman Maclean, A River Runs Through It
Below are a couple of fly casting instructional videos by Orvis that you might find interesting.
Below is an entire fly casting series by Orvis that you that will help develop your skills.