Start with a clean, untreated piece of wood about 1 inch thick and long and wide enough to completely hold the item you are going to grill. Typically people use cedar, but many woods are good like alder, oak, maple, cherry or apple. Any wood good enough to smoking is good for plank grilling, but make sure that there are no chemical treatments on the board. You can buy cooking quality wood planks either online or in many specialty food stores.
It is probably your experience that wood burns. To reduce the burning of the wood to a point where you can effectively grill on a plank you need to make sure that it has been soaked in water for at least an hour. This will get the wood as wet as it can get and give you the time you need to get your fish completely cooked before the board starts really burning. If you notice that the board has caught fire while you are grilling, spray it down with water to put out the fire. This isn't to say that you don't want the board to burn a little. The smoldering of the wood is what creates the smoke and flavors the fish. You just don't want the board actually on fire.
To prevent your fish from sticking to the board, very lightly brush it with cooking oil on the side that the fish will sit. You do no flipping when plank cooking. Plank cooking is indirect because the food is insulated from the direct heat. You do want the board exposed to the direct heat of your grill so that it can smolder, so this is style of grilling is a very basic process as far as the grill goes. And since you won’t be flipping the fish or really doing anything with it during the cooking this is a very easy way to prepare grilled fish.
Once you have the grill burning and the planks soaked place the fish on the board, season as appropriate and place the whole thing on the grill. Because the fish is being cooked indirectly it will take longer than if you just grilled the fish directly. Plan on about 50% more cooking time versus regular grilling when cooking on a board. During the cooking time you can baste the fish with lemon juice, butter, or most anything that isn't flammable. You do not want to inspire a fire.
Once the fish is done you can remove the whole plank and fish with a pair of grilling mitts or you can slide the fish off onto a platter. You get on use out of each plank. If you are using a gas grill you should get the plank off the grill pretty soon because you don't want a lot of ash falling into the grill. If you are using a charcoal grill you can just let it burn off and clear out the ashes later.
Plank grilling really is a great way to grill. The flavors and the ease have always made this method popular. Once you've given it a try you will want to grill lots of dishes on a board. You can plank grill roasts, poultry or most anything, particularly those things that require a longer grilling time. Quick items won't gain much from the plank because they won't be exposed to the smoke long enough to get the flavor. Also, you don't want to plank cook items that need to be grilled hot and fast like steaks or chops.

