There are two main ways to remove the excess salt from salt fish. As a rule, the aim is never to completely remove all the salt from the fish, there should always be enough salt remaining to taste so that the salt fish has some flavor. The process of removing the excess salt from the salt fish also rehydrates it.
All salt fish are not created equal - some are more salty than others. It is important to taste the salt fish after the initial stage of soaking or boiling to ascertain whether or not you should move on to another stage of de-salting the fish.
Method No. 1
Place the fish into a large bowl and pour boiling water over the fish. The water should cover the fish. Cover the bowl and let the salt fish soak overnight. The following morning, drain off the salty water. Remove the bones and skin (if using bone-in salt fish). Pry off a piece of the fish from the meatiest part of the fish and taste it. Do not taste the top piece of the fish that has been directly exposed to the hot water, taste the inner piece, that is the best gauge as it will tell you how much the hot water really penetrated the saltiness of the fish. If it tastes very salty, add the fish to a pot and pour in hot tap water to cover the fish. Set on high heat and bring to a boil. Let the salt fish boil for 20 minutes; drain, and when cool enough of handle, proceed with the recipe as instructed for whatever dish you are planning to make.
Method No. 2
Add the salt fish to a pot of hot tap water. Let the water cover the fish. Place on high heat and bring to a boil. Let it boil for 25 minutes. Drain. Add a fresh batch of hot tap water. Cut up a whole lime or lemon into wedges and add to the pot and bring to a boil. Let boil for 20 minutes. Drain, and when cool enough to handle, remove the bones and skin (if using bone-in); proceed with the recipe as instructed for whatever dish you are planning to make.