On the flats or shallow clear water, toss your fly well ahead of the fish, cutting the chances of spooking it. In brown or dirty water where sight-casting is impossible, look for a stream of bubbles, caused by air leaving the fish's bladder. You'll also see them roll for air. Cast your jig far enough ahead of bubbles to intersect the approaching fish, allowing enough time for it to sink to the tarpon's feeding depth (near bottom).
When casting jigs, the lure is brought back with a quick lift of the rod, reeling as the rod is lowered for the next lift. If your jig feels funny, either "weightless" or "logy," at any point in the retrieve, immediately set the hook-- hard. Tarpon will hit a jig as it falls, often spitting it before you can come tight on them.
It the tarpon is hooked, it'll jump, possibly 10 feet into the air. As the fish falls, "bow" to it by leaning toward it and pointing the rod-tip at the tarpon. This lessens the chances of line breakage due to the weight of the fish falling upon it. If the fish is still hooked, consider it good fortune. After a few more jumps, the tarpon may settle under the skiff and tow you. Lift on the fish from its side, either left or right, and keep steady pressure. After five minutes, change sides, pulling on the tarpon from the opposite direction. This seems to tire a fish quicker and works with many light-tackle species.