Your fish should have an acclimation (to adjust for differences in temperature, salinity, and other chemistries (e.g. display tanks, especially reefs, tend to use up more calcium and carbonates then quarantine tanks). Assuming you used water from your display tank, this can be done quickly (<1 hour). Try to make sure your hospital tank water has the same or slightly lower salinity.
There are lots of ways to bring the salinity down. There is no right way as long the salinity drops gradually.
If you are using an uncycled tank be prepared for lots of water changes.
When I have done hypo I would start by mixing up a large batch of 1.009 water. I would then do a 20% water change by taking out the water quickly then every 1/2 hour I would add back ~1/5 of the water. When you get closer ~specific gravity 1.014 (~4-5th water change depending on your starting salinity) I would start by adding aged freshwater. Let the fish rest for a few hours before starting the next cycle.
An alternative would be to use just freshwater but to use a smaller amount of change (e.g. 10%) for the first 4-5 water changes. I would tend to recommend this method if your tank has already cycled.
Make sure you watch your ammonia, nitrites and pH. As long as these stay under control, hyposalinity is very safe.