To start with, you need a few basic tools.
A good serrated knife, a flexible filleting knife, a pair of fish pliers (clean needle nosed pliers are fine) a chopping board and some clingfilm.
Oh yeah, and a fish...
If you've bought the fish whole then it's very likely not to have been scaled. Unless you plan on skinning the fillets once you've taken them off, its a good idea to scale the fish now. Trying to scale fillets is possible but ruins the flesh.
To scale the salmon, clear away everything around your sink. The scales will flick everywhere so it's best to get as much stuff out of the way as possible or you'll be finding scales in unlikely places for weeks.
Always scale the fish from tail to head. This is against the direction the scales grow and allows you to get a knife in under them.
Hold the knife at roughly 45 degrees to the fish and scrape up towards the head in short, sharp movements. Only try to scale a small area at a time. You may find that a stiffer bladed knife is better for this job than a filleting knife.
Make sure you scale right up to the gill flaps and around the fins along the body of the fish. wipe the knife blade off frequently with a piece of paper towel. Try not to get too many scales in the sink... you'll only have to pick them out of the plug hole later!
Once the fish is scaled, give it a good rinse over the outside running the water from head to tail.
Also, give the body cavity a quick rinse, but dry it with kitchen towel to avoid letting too much water seep into the flesh.
Place the fish on the board and pick up your serrated knife. Feel just behind the gill flaps on the fish's body and you'll find a bony part, right next to the gills. Place your knife here, running alongside the bony part.
Take a firm hold of the fish and using the serrations of the knife, cut straight down through the fish's neck, taking care to keep right behind the front fins.
Discard the head, salmon doesn't make a good stock anyway and the head can make it taste bitter.
Now you should be able to see the backbone of the fish, looking in from where the head was.
Take your serrated knife again, and start cutting the top fillet off by running the knife along the back bone of the fish, sawing as you go.
Watch the knife coming out of the top of the fish, it should just shave past the dorsal fins. Keep cutting all the way to the tail of the fish. You should easily be able to feel the knife running along the backbone as you cut.
When you've reached the tail, keep cutting, the knife will pass through the last bit of the fillet and then you can just lift the top fillet off.
To take off the lower fillet, turn the fish over onto the bone.
Again, take your serrated knife, cut along the spine, but this time, use the fingers on the hand holding the fish to lift the belly flap up out of the knife's way.
Lifting the belly up like this stops the knife chewing into the belly flesh and shredding it.
Once you have reached the tail, you will be able to lift the bones clear of the fillet.
To finish and prepare the fillets, they need to be trimmed and boned. Carefully lay the fillet on the board and check for loose scales of bits of bone and remove as needed.
First, using the filleting knife, trim away any excess fatty tissue from the top of the fillet. The fatty stuff sometimes runs down onto the fillet as well, so this will need to be trimmed off with a sharp knife.
Now, feel along the belly with your fingers and find the rib bones. Using a sharp filleting knife, insert the edge of the blade under the ends of the bones, then use an smooth slicing action cut the bones away from the flesh. To minimise wastage, use an upward pressure on the knife and angel it towards the bones so you scrape the flesh off as you cut.
Once the ribs are removed, trim the belly back to neaten the fillet. The flesh down here is very fatty and you should use your own judgement as to how much to trim off.
Now comes the fiddly bit. You now need to remove the 'pin' bones that run along the length of the fillet to about 3/4 the way down. This is done easily with a pair of pliers.
First, run your fingers, just above the spine-line along the fillet. You should be able to easily feel the bones sticking in the flesh.
Using the pliers, gently grasp the end of the bone, tying not to nip the flesh as it will tear and leave a hole.
Now gently pull the bone out of the flesh. Make sure you pull at an angle of roughly 45 degrees TOWARDS the head of the fish or you'll just tear a hole in the fish as the bone comes out.
Repeat this process all the way down the fish until you can't feel anymore bones.
And there you have it, one fillet ready to be cut for steaks or poached or frozen whole... but we'll save that thread for another day, I think...