How long should tilapia filets of normal thickness be broiled?
Broiling fish is extremely easy, although I would recommend saucing the fish after it is cooked as your BBQ sauce will most likely burn under the heat from the broiler.  Your food should be about 8 to 12 inches away form the heat source, but most under oven broilers have a fixed height away from the flame.  You need to make sure that your fish is fully scaled before cooking and you should season it with salt and pepper as well.  Lay the fish on a pan, making sure that you lay it skin side down and that there is room on each side of each piece.  Turn on your flame and slide the fish under the broiler, remove when the fish is flaky, white and lightly browned on top. If you are unsure if it is done, take a fork and twist it in the flesh of the fish and it should flake away fully white, it's done.

Then add your sauce and serve.

Additionally, BBQ sauce will mostly overpower the flavor of your tilapia, you might find that whipping up a butter sauce or a white wine sauce will suit you better.  Also, alot of fish does well with just a little salt, pepper, and lemon juice.