Salt is a contaminant, and contaminants are quite pernicious. A thimble full of saltwater in a freshwater ocean? Now its a saltwater ocean!
To desalinate: abuse screwpumps, or flush with a freshwater river (new to current release)
Basically, construct a cistern that has *never* come into contact with water, *ever*. Pump water into the cistern. Magically, through an as yet unknown magical principle of screwpump technology, the salt is not carried, and the cistern will be full of fresh water.
Just ensure that no salty water of any kind comes into contact with the cistern. (This means DON'T let dwarves wash at the well! Salt water contaminants on clothes washing back into the well head contaminates the well, BOOYA, now its salty!) If salt contaminant hits a wall or floor tile, it will always be salty from that point on. To wash dwarves, use benign 1z waterfalls and mist generators.
Alternatively, use DFHack to remove all the contaminant flags from water. (Added because of stagnant water plague in previous releases; stagnation creep was 'fixed' with the moving water code, which also keeps rivers that spill into oceans from being tagged as salty. Prior to this, freshwater was very rare indeed on coastal embarks! To address this, dfhack added a tool to cleanse water supplies.)
Screwpump desalinator is the best non-cheaty method left for you, unless you have an underground river you can exploit.