If you want to cure your fish (basically a brine without moisture) it is dependent on the thickness of the meat mostly. If it's as thin as 1/4", it will take approximately 1-2 hours. If it's more around 1" thick, it could need 3-8 hours.
If you use a dry-cure method you don't have to worry about having too much salt because once you're done, you just wipe it off.
If done incorrectly (ie. not enough time), you should notice a difference in the colour between the edge and the interior. Typically, the colour becomes more pale.
The main purpose of the salt is to dehydrate the meat, not necessarily drying. If you use a brine, it obviously won't become dry.