(assuming right handed cook)
knife in right hand
fish in the left.
Never put your knife down.
Pick up fish, place it on board, wipe it down on both sides.
with the fish spine towards you, hook gills over the right edge of cutting board, with spine as close to the edge of table as possible.
Hold fish with left hand, with a clean dry cloth.
Starting just behind the gills, cut down at an angle towards the point of the spine where the gills "meet" behind the head.Stop at the spine
Turn blade towards tail of fish, with your blade resting horizontally against the spine.
Holding belly of fish out of the way with your left hand, begin long purposeful slices towards the tail, keeping your blade against the spine of the fish. Do not lift handle of knife, or tip of blade... keep it level.
You will hear a clicking as you do this, this is good.
Continue until you reach the tail.
do not set your knife down.
Wipe down board.
flip fish over, hooking gills on left side of board, spine towards you.
repeat in the opposite direction. Remember to hold belly out of the way with your left hand.
If done correctly, there will be very little flesh left on the carcass of the fish, and the filets will havesome evidence of the spine running down the centre of the filet.
Set carcass aside.
Place filet in front of you with bone side up. I do it with the ribs facing me. Cut the ribs off in one piece by getting under them and removing them with a thin bladed knife.
Remove any "spine" in the same manner.
Bones for the stock pot.
Place filet on board with tailend to your left.
about 1/2 cm from end cut down into flesh, stopping at skin, turn blade toward head end, laying blade flat against skin (actually with blade facing slightly down towards cutting board)
Grab tail end of skin in left hand, using a dry cloth .Holding knife still, gently pull to your left while using a slight sawing motion with your left hand... your knife doesn't move.
Skin should be clean. No flesh.
Use fish tweezers to remove pinbones. Pull bones straight out... not up, not back, not forwards... straight out.
Feel for them with your fingers.
Anyone can cook salmon with bones in... people pay for food expecting something better.
Now, grab a metal spoon, and scrape all the flesh off the carcass.
the head and spine hit the stock pot... or, if you want to score points with the Chinese ladies in the Stewarding department, give them to them.
This is what a fish knife is for. Right tool for the job. I've done a ton of fish with both a fish knife and a 10 Chef's knife... give me the fish knife any day. Both work... one works better.