If the tank is already cycled, add 6 grammes of marine salt mix per litre of water into the tank and stir well. You may want to make up a brine solution first, and then dribble that into the tank. Either way, that should raise the specific gravity to about SG 1.003 at 25 degrees C. This will low enough not to stress the filter bacteria, but high enough you can settle the mudskipper in easily.
Now you can add your mudskipper. Over the next few weeks, each time you take out some water, replace it with water containing 9 grammes of salt per litre. With each water change, this will nudge the salinity upwards until it is eventually SG 1.005 at 25 degrees C, enough for most mudskippers to feel comfortable. You may decide to raise the salinity further, to about SG 1.010 at 25 degrees C if your mudskipper doesn't look happy, but when raising the salinity above SG 1.005, it's important to keep track of ammonia or nitrite, just to make sure the filter is adapting.
To be fair, mudskippers are highly tolerant of ammonia, and since they spend almost all their time out of the water, they're less vulnerable to water quality problems than most fish. But as always, good conditions help.
Do read Richard's chapter in my book for details. Either buy or borrow the book as you prefer. He's written by far the longest and most detailed review of these fish, and I'm sure you'll find what he has to say about behaviour, diet, etc., very helpful.
Cheers, Neale
