Lesson 1: How to cast a fly rod, for beginners

If you can do this,
you can cast a fly rod.

If fly fishing were difficult and required a ton of skill, I couldn't fly fish.  It does take some practice, but almost anyone can do it.
If you've ever hung a picture on a wall, or nailed a board to a fence rail, you can cast a fly rod. That's because the motion your arm makes when casting a fly rod is the same motion your arm makes when swinging a hammer at a nail that's roughly at eye level.
(If no one is watching, stand up and pretend to strike a nail that's in a wall about the same height as your eyes.  You swing the hammer back, accelerate forward, and then stop at the nail.  You don't swing through the wall, because you'd tear up the wall.  And you don't use a ton of force, or you'd punch a hole in the wall.  Casting a fly rod uses a very similar motion.)
Fly rods are designed to flex, and this bending does most of the work for you.  You don't have to "throw" the fly across the creek; the rod's flexibility will increase the force, and, along with the weight of the fly line, will cast the fly where you want it to go.  A lot of beginners don't let the fly rod do its part of the work; they think they have to 'muscle' the fly when casting.
That's the end of  Lesson 1.  We'll build on this foundation in the following lessons.