All good tips.
My order or importance:
1. Stay relaxed - Ray used to say "steel your nerves!" Focus on the job and make the cast. Always look at your line loop while false casting; the loop size will tell you if you're doing it right or wrong. Tip cast for tight loops, especially into the wind. The quicker you stop the rod tip, the tighter the loop.
2. Don't overcast; and especially don't have the fly attacking the fish. Look at the spot you want your fly to land, not at the fish. New anglers to tarpon fly-fishing tend to look at the fish and then they bean it. Also note the tidal current speed and speed of the fish and try to adjust for drift and closing. Laid up fish are another thing: you want the fly to land close but in a position to be moving away from the fish when it wakes up on the splat. I like to drop the fly about a foot from the poon's eye if I can.
3. Don't cast too soon unless your guide tells you to fire. Ray always had me start throwing at around 70 because he knew I could make the cast and could lift a lot of line for a re-cast if needed. However, if a fish just showed up close to the boat, coming off the grass or whatever, don't wait for the guide to tell you to cast - just do it anyway you can, like NOW! - get the fly in front of the fish. Lot's of times you don't see the fish until you're damned near on top of it.
4. Keep stripping until the line comes tight unless you know it won't come tight (fish eats and keep swimming straight at you) then you have to try something. I use the "Scissors Strike" Strip hard and swing the rod low and to my right since I'm right-handed.
5. Pray to the Fishing Gods for good luck! Good luck is the most important thing of all ;-)