Methods of cooking fish which are amenable to making the exterior crisp or crunchy would be baking, broiling, or grilling, which are all forms of dry heat cooking. You must compensate for the dryness of these methods, though, as fish – even salmon, one of the fattier fishes – have little of the interior fat which keeps meats moist.
Leaving the skin on enables the cook to prepare it so the skin is crispy. Some people don’t care for fish skin, doubtless because they’ve only had it mushy. Cooked properly so it’s crispy, fish skin is delicious. Marcus Samuelsson has a recipe for salmon in his book Aquavit in which the skin is cooked separately so it’s almost like bacon, and then used as a garnish. Sounds good to me!
One way to make the exterior of fish crunchy is to batter or bread it. However, I’ve yet to come across any recipes that treat salmon in this fashion other than a layer of crumbs on fish cakes. And I do love salmon cakes, which are good with canned salmon and fantastic with fresh. But you didn’t mention fish cakes.
Nuts make a nice topping; my thoughts turn first to pecans, then to almonds for a second choice. They can be applied before the fish is cooked (you’ll have to be careful not to burn them), or browned and added after.
Assuming we’re talking about salmon filets or steaks as opposed to the whole fish, to bake, I’d put it in a baking dish just large enough to hold the piece(s) of fish, and pour in a little fish stock or white wine, or a little of each, enough to moisten the bottom of the pan. Cover the top with buttered bread crumbs (fresh are preferable to dry — either sauté them in butter first, or mix them with melted butter), and bake uncovered at 350°F until done. Be sure to preheat the oven. The general rule of thumb is to cook fish for 10 minutes per inch of thickness, but I’ve found in the oven it takes a little longer. I’d say start with 15 minutes, and keep checking at five minute intervals after that if it’s not done.
If you choose to broil, preheat the broiler for at least 15 minutes. Don’t use breadcrumbs or nuts if the salmon is thicker than 1″; they’ll burn before the interior of the fish is done. Simply season the fish, dot with butter, and broil until done; you won’t get a really crispy exterior, but it won’t be soft, either. Same thing with using the grill, only oil the fish rather than using butter.
You can pan-broil it, which I usually do in preference to grilling. Heat a cast iron or other heavy skillet over low heat and then turn the heat up under the pan to high. Oil the salmon, and place in the pan. Leave it to get a good sear before turning to sear the other side. At that heat, it won’t take long to cook through.
A more unusual technique would be to thickly coat one side of the fish with a flavored salt (a smoked variety would be especially tasty), and sear on one side until crisp in the above-mentioned pan to which you’ve added a thin layer of an oil. Use one which can take high heat, like grapeseed oil, and heat it to just below the smoking point. Without turning the fish, finish cooking it in a 450°F oven. The seared side will be crusty and the top juicy. Because the salt will somewhat protect the surface of the fish, figure about four minutes of searing and another five minutes or more in the oven.