How to Fillet a Salmon 
www.great-lakes.org
Here are 7 simple instructions on how to fillet a salmon supplied by the people at www.great-lakes.org.
After catching your salmon or purchasing a fresh one from your local market, be sure to bleed it and immediately place it on ice. Allow the salmon to go through rigor mortis before attempting to fillet it otherwise the fillets will contract and become tough after filleting. Start with a very sharp 8 to 10 inch flexible knife and an ice pick. There are many different knives that will work well for filleting salmon. The type most recommended is an 8" long blade that's narrow and fairly flexible. Knives come with all different kinds of handles and blade shapes. You don't need to spend a fortune to get a knife that will work well but expect to pay $20 - $30 for a good fillet knife.
Step 1.
Make the first cut just behind the gills of the salmon. Slice down the bone then, without removing the blade, turn it and slice straight along the backbone..
Hint: You want to use the backbone as your guide but don't cut through the backbone.
Step 2. ...to the tail. Note that the fillet has been cut away from the rest of the fish. After slicing fillet off at the tail, turn the fish over and repeat the procedure on the other side.
Step 3. With both sides removed, you have cut away both fillets without distrubing the fish's entrails. This is the neatest and fastest way to prepare fish. Now to finish the fillets...
Step 4. Next step is to remove the rib section. Again, a sharp flexible knife is important to avoid wasting meat. Insert the blade close to the rib bones and slice the entiresection away. This should be done before the skin is removed to keep waste to a minimum.
Step 5. Removing the skin from each fillet is simply a matter of inserting the knife at the tail and "cutting" the mea from the skin. With the proper knife it's easily done.
Step 6. Here is each fillet, ready for the pan or freezer. Note there is no waste. Remember not to overwash fillets. This will preserve tasty juices and keep the meat in its firm natural state.
Step 7. As a precaution, cut away about one inch of the belly and dorsal sections (top and bottom) of the fillet. The belly and dorsal sections have more fat and protential contaminents. Furthermore, it's recommended to scape off any traces of the blood line. Remember, follow your states guidelines to eating fish and follow these instructions on how to fillet for boneless and safe fish.