The trick to casting a fly rod well is generating plenty of line speed.
Line speed not only adds distance to a cast, but—with the fast-action, quick-recovery rods most anglers use these days—it is also the key to accuracy. If you're not generating enough line speed, you simply aren't using a fly rod to its full effect.
It's a pretty simple deal if you focus on the three basic steps.
1. Start the backcast with the rod tip low to the water. Doing so uses the surface tension of the water to flex and load the fly rod. If you start the cast with the tip high, you have less leverage.
2. Accelerate and stop. Build into the backcast and stop the rod high. If you don't stop the rod, you let all the cast's energy pour out of the back. Think of it as if you're lifting a glass of water off of a table and then throwing it over your shoulder.
3. Haul. Pull on the line with your non-casting hand as you make your false casts. Many novice anglers are intimidated by the idea of double-hauling, but it doesn't have to be complicated. Even tugging the line a few inches with your fingertips will boost line speed. You don't need to haul in bunches; a little bit will help you develop the timing, and you can build from there.