Place the salmon in a container large enough to cover it with about 1-inch (3-cm) of water. Add 2 teaspoons of salt to the water and gently swish it around with a spoon to mix and dissolve. Let the salmon sit and soak for 30 minutes.
Remove the salmon from the salt water. Hold it under cool running water to rinse well, then pat it dry with paper towel. Dump the salt water out of the container, then rinse, and dry.
In a small bowl, mix the sea salt, sugar, and pepper.
Place a layer of dill fronds inside the clean container. You want the layer to be large enough to cover the bottom of the fish. Rub some of the salt-sugar mixture on the bottom of the salmon, then lay it down on the dill. Use the rest of the salt-sugar mixture to cover the top and sides of the salmon. Cover the top and sides of the salmon with more fresh dill until you can't see the fish. Lay a piece of plastic wrap gently but snugly over the dill and salmon. Place a weight on top of the fish (I usually use a loaf tin with a large can inside of it) and place the entire container in the fridge overnight.
The next day, remove the weight, plastic wrap, and dill from the top of the fish. Flip the salmon over. Replace the dill, and re-cover the fish with the same plastic wrap. Place the weight back on top of the salmon and put it back in the fridge, again overnight.
Remove the fish from the container. Remove all of the dill fronds, then rinse the salmon under cool running water. The more you rinse the less salty your fish will be. Gently pat the fish dry with paper towels, then carefully slice it thin with the sharpest knife you have. Serve immediately or refrigerate for later. Cured salmon is best served at room temperature.