Assuming you're throwing a crab pattern, my preference is to try to cast the fly as close to the fish's head without spooking it (as Geoff says, "spook 'em or catch 'em"), then let it drop if you think the fish has seen it.  If the fish tails on it or seems excited, I would give one long strip, being careful not to strip too fast or too slow--kinda medium (easier said then done!).  If you feel the line come tight, then you're in business!  If you think the fish hasn't seen it, but the vector of the cast is good, I would strip (short...maybe 6 or so inches at a time) a few times to try to excite the fish.  When he sees it, again, let it fall to see if he'll tail on it. 

Sometimes the fish will look at it hard then swim away, as permit often do (act like permit!) ???.  I guess it depends on weather, wind, and sunlight.  The calmer brighter conditions are obviously gonna be tougher.  > or = to 10-15 knot winds that cause a 'riffle' on the surface with some clouds around is probably optimal.  There will be other times that even an errant cast will make the fish turn around and eat.  Just try to keep all the slack out of the line and monitor how fast the boat is moving toward the fish--the speed and length of your strip will depend directly on how fast the boat is moving.

If you're throwing a shrimp pattern or a clouser, I would cast close to the fish and keep stripping.  Needless to say, that kind of bait swims and doesn't usually fall to the bottom like a crab.  In the Yucatan in Mexico, some of the guides actually preferred shrimp patterns.

Clear Monic fly line may also help increase the number of hook-ups.