Cleaning and Filleting a Fish
First, remove the fish's fins with scissors if desired. Be careful, as some fins can be quite spiny. (If you plan to cook the fish whole, leave the fins intact for a more dramatic presentation.)
Next, using a fish scaler or the blunt edge of a knife blade, scale the fish: Hold the fish by the tail and let it hang down into a plastic bag or a sink full of water. (The scales will fly in all directions.) Starting at the tail end and working down to the head, scrape the scales from the fish and rinse it well.
Clean the fish by cutting into the cavity from the belly side, the anal vent up to the head. Remove and discard the entrails and rinse the fish well.
Here are the basic steps for filleting a round fish:

Place the cleaned fish on a cutting board at an angle, with the head pointing away on your right (if you are right-handed) and the back facing you. Using a sharp boning knife, make a crosswise cut just below the gill to separate the flesh from the head. Now, starting at the head, run the knife along the back, cutting through the skin, until you reach the tail. Make a crosswise cut to separate the flesh from the tail.

Retrace the cut along the back, cutting in with long, smooth strokes until you feel the backbone with the tip of your knife.

Lift up the edge of the flesh, revealing the ribs. Cut the flesh away from the ribs, starting at the back and following the curve of the ribs with the knife. As you cut, keep the knife in contact with the bones to remove as much flesh as possible. Do not remove the fillet from the bones yet, as you will need the bulk to fillet the other side successfully.

Turn the fish over and make crosswise cuts to separate the flesh from the head and tail. Starting at the tail end, make another cut along the backbone. Proceed as directed in Step 3, cutting the flesh away starting at the backbone, then up over the ribs and down to the belly cavity. Remove the fillet from the bones. Turn the fish over and lift off the first fillet.