This is the salmon I brought for trapeza on the Entry of the Theotokos. There's a link to a website below that explains all about it, but basically, this is what I did: Find a glass container large enough to hold the entire fillet, laid out flat. Cover the bottom of the dish with a layer of coarse salt (like Kosher). Rinse off the (thawed) fillet of salmon and lay it, skin-side down, on top of the salt. Cover the top and sides of the fillet with more coarse salt. (I sprinkled some lemon juice--maybe a TBS?--over it as well.) Cover with plastic wrap (or use a lidded dish) and put in the fridge. Let it sit for about 24 hours, checking now and then to make sure all the fish is covered by salt. At around 18 hours it might develop a brine--this is fine--just spoon it back over the fillet. After 24 hours or so (taste a bit to see if it's "done"), brush off the salt and rinse the fish under cold running water (if you're afraid it'll be too salty, you can soak it in cold water for a bit). Thinly slice, and eat! It was so, so good.
I think my fillet was about 1.5 pounds, and I used about 1.5 cups of salt.
Please read the blog post below for more information!