Cure the Fish. Mix together the brine ingredients and place your fish in a non-reactive container (plastic or glass), cover and put in the refrigerator. This curing process eliminates some of the moisture from the inside of the fish while at the same time infusing it with salt, which will help preserve the salmon.
You will need to cure your salmon at least 4 hours, even for thin fillets from trout or pink salmon. In my experience, large trout or char, as well as pink, sockeye and silver salmon need 8 hours. A really thick piece of king salmon might need as much as 36 hours in the brine. Never go more than 48 hours, however, or your fish will be too salty. Double the brine if it's not enough to cover the fish.
Dry the Fish. Take your fish out of the brine and pat it dry. Set the fillets on your cooling rack, skin side down. Ideally you'd do this right under a ceiling fan set on high, or outside in a cool, breezy place. By "cool" I mean 60°F or cooler. Let the fish dry for 2 to 4 hours (or up to overnight in the fridge). You want the surface of the fish to develop a shiny skin called a pellicle. This is one step many beginning smokers fail to do, but drying your cured, brined fish in a cool, breezy place is vital to properly smoking it. The pellicle, which is a thin, lacquer-like layer on top of the fish, seals it and offers a sticky surface for the smoke to adhere to. Don't worry, the salt in the brine will protect your fish from spoilage. Once you have your pellicle, you can refrigerate your fish for a few hours and smoke it later if you'd like.
Smoke your fish. Start by slicking the skin of your fish with some oil, so it won't stick to the smoker rack. Know that even though this is hot smoking, you still do not want high temperatures. Start with a small fire and work your way up as you go. It is important to bring the temperature up gradually or you will get that white albumin "bleed" on the meat. I can control my heat with my smoker, so I start the process between 140°F and 150°F for up to an hour, then finish at 175°F for a final hour or two. NOTE: What my smoker is set at is not necessarily what the actual temperature is. Smoking is an art, not a science. To keep temperatures mild, always put water in your drip pan to keep the temperature down. If your smoker is very hot, like a Traeger can get, put ice in the tray.
Baste the Fish. After an hour in the smoker, baste the fish with birch or maple syrup, or honey; do this every hour. This is a good way to brush away any albumin that might form. In most cases, you will get a little. You just don't want a ton of it. Even if you can't control your temperature this precisely, you get the general idea. You goal should be an internal temperature of about 130°F to 140°F. (Incidentally, yes, I keep the smoke on the whole time. I don't find this to be too much smoke, but if you want a lighter smoke, finish the salmon without smoke or in a 200°F oven.)
You must be careful about your heat. Other than failing to dry your salmon long enough, the single biggest problem in smoking salmon is too high heat. If you've ever seen salmon "bleed" a white, creamy substance, that's a protein called albumin. If you see lots of it, you've screwed up; a little is normal. Here's what happens: If you cook a piece of salmon at too high a heat, the muscle fibers in the meat contract so violently that they extrude albumin, which immediately congeals on the surface of the fish. It's ugly, and it also means your salmon will be drier than it could have been. You prevent this with a solidly formed pellicle, and by keeping your heat gentle. If you let your heat get away from you and you do get a white mess on your salmon, all is not lost. Just flake it out and make salmon salad with it: The mayonnaise in the salad will mask any dryness.
Cool and Store the Fish. Once your fish is smoked, let it rest on the cooling rack for an hour before you put it in the fridge. Once refrigerated and wrapped in plastic, smoked fish will keep for 10 days. If you vacuum-seal it, the fish will keep for up to 3 weeks. Or freeze your fish for up to a year.