I have never done tilapia on the grill. At which temperature, and how long should I cook it?
Agree with @Daniel that fillets can be done on the grill, but in my experience a tender fish like Tilapia will break up and fall through the grill. Unless you have a finely meshed grill and a lot of cooking experience I would avoid it.
Tuna, swordfish, mahi-mahi and salmon steaks all work well on the grill. But this should not stop you from grilling Tilapia or any other tender fish, just put it on the grill whole! For Tilapia I would do something like below.
Make shallow slashes in the thickest parts of the flesh, coat with olive oil, season with your favorite spices, and then grill for 3 to 5 minutes max each side on a hot grill. You can mostly judge by sight. When it still looks like it needs another minute I always sacrifice my piece, take it off the grill, and pry off one of the thicker parts. If it's still raw looking on the inside, let it and the others go for another 30 seconds on each side. Nothing better than perfectly cooked moist fish and nothing worse than dry overcooked fish and the difference between the two can be as little as 1 minute. Note: it might be obvious to many, but using a whole fish implies that you've "cleaned" the fish first by removing it's innards before any other preparation.
If you really want to do fillets for a delicate fish on the grill then just coat them in oil, and wrap in tinfoil with a slice of lemon or whatever you prefer. Again, sacrifice a piece to check for doneness. Tinfoil will not magically keep the fish moist if you overcook it. Using foil you won't get the flavor of the grill, but then again picking all the broken pieces of each fillet off the hot coals is a bit too much grill flavor IMHO.
Very hot, and until it's done.
I'm not being a smartass here, I'm being serious. When grilling (especially fish), you generally want your grill as hot as possible; you want to promote the Maillard reaction quickly, in order to get nice grill marks.
Tilapia fillets are generally extremely thin. A minute or two per side should do it. The secret with grilling fish is to put it on and then don't touch it. If your grill is properly seasoned and your fish is dry (important! you don't want water here, it will make sticking worse) the fish will pull away from the grill cleanly when it is done on each side.