There are many types of nuclear desalination, and some will be referenced in this discussion. Before trying to describe the specifics, one should understand why nuclear desalination is a good option. There have been doubts in the past about this method, but many can be explained away.
Nuclear energy has the lowest cost source for large amounts of energy, except for the best of the fossil-fuel resources. Another point is that the cost is not relevant to the location of the plant. There are many statistics to support this statement. It still seems to be holding even though the cost of nuclear energy is rising as it becomes unfavorable on the market.
The economics of nuclear energy could be greatly improved through engineering advances if the effort was made. New methods and improvements are always being discovered and it seems that with the trends of improving the up-scaled processes that nuclear energy is a very good choice for desalinating.