Place salmon fillets, skin side down, on a sheet of aluminum foil large enough to completely wrap around the salmon.
Cover salmon with a thick layer of the sea salt. Use more salt as needed, depending on the size of your fillets. If using smoked salt, sprinkle it evenly over over the salmon.
If using multiple fillets, sandwich them together, skin side out. Wrap foil around the fillets. Wrap them again with another piece of foil.
Set wrapped salmon on a baking sheet or any lipped container-- the juices will leak out, so you want them contained. Set the salmon and lipped container inside refrigerator. Set something heavy on top of the salmon- such as a cast iron pan or brick.
Leave salmon to cure for 24 hours, and then remove from foil. Rinse the salmon for several minutes to remove salt.
Use a fillet knife to slice salmon as thinly as possible, cutting across the top of the fish in long thin slices, removing the skin with the last cuts. Your knife blade should be parallel to the grain of the fish, not perpendicular. If your fish is falling apart as you cut-- you're probably cutting it from the wrong direction. If you're cutting a whole side of salmon- you should be cutting head-to-tail instead of side-to-side. If you don't have a fillet knife, dice the salmon instead.
Place salmon slices in a covered dish, and put back in the fridge for at least eight hours to allow the salty flavor to balance out.
Salmon will keep in the fridge for about 2 weeks.