Once fish have been spotted, it is important to quickly and accurately place the fly/lure in front of the fish's path. Tarpon are not easily spooked and you can place the fly/lure quite close to the fish. A distance of about three to five feet is perfect. Allow it to sink to the level of the fish and then begin to strip to retrieve it at a moderated pace. If the tarpon is in the dining mood, it will take the presentation. If you get refusal, just continue to cast until you get its attention. If you get refusals from several different fish, change flies.
Tarpon have concrete lined mouths, so a super sharp hook is an absolute necessity. Correct hook setting will also help put the odds in your favor. If fly fishing, point the rod tip at the fish and firmly set the hook with your stripping hand only. Then keep your rod tip close to the water, to eliminate slack, and pump the rod sideways with short, sharp tugs as you pull on the line and the rod simultaneously. This sounds very nice on paper, but the sight of a tarpon inhaling your fly can cause even the experienced fisherman to lose his cool and occasionally choke.