Learning to Fly Cast
Learning to cast a fly rod is a bit about practice. First, the practice must be on dry land. Don't even think of starting this process in a stream or any other body of water.
Finding a Place to Practice the Fly Cast:
The only really important things is that you have space and that you will not be likely to ruin your line. The amount of space you will need will be approximately 40 feet in front and behind you. A nice grassy field is ideal.
You need to have your line, including backing, fly line, and leader installed and ready to go. I suggest that you use a knotless leader system, especially at this stage. A good bet is the Reconnect System from Scientific Anglers. These leaders are very easy to use and can be attached without knowledge of any advanced knots.
Observe Video Instruction on Basic Fly Casting: