How can I keep delicate food from sticking to the grill?
Other people have answered similarly but definitely make sure your cooking surface is VERY HOT before the food hits the surface. Cold food+cold metal=sticking!  

In addition to this, you should also make sure you don't start trying to flip too early. Let the food cook and get a good sear on one side before you try to flip. If you do this with a hot surface, you shouldn't have any problems with sticking.

One more thing, it's important that the grill surface is clean, so cleaning your grill religiously after you finish using it each time, and then oiling it lightly before you use it, can be a huge help in this area.