My approach with ostreopsis dinos in one tank was very successful, eliminating them completely in 2 weeks.
First, get phosphate and nitrate to the proper range as described above.
Second, get some Red X by Fauna Marin. It's safe and works. Dino X, from the same company, also works but is reported to be less safe for corals (although in many cases this may be due to people not following directions precisely.)
Third, start adding small doses of live microalgae on a regular basis. (I prefer this to diatoms.)
Finally, and this is the big one, begin daily siphoning of dinos through a 1 micron filter bag. Siphon until you've removed most visible dinos, then return the filtered water to the system. Even after doing this just the first time, you will see corals perk up as all those nasty dinos and their toxins are manually removed. 1 micron filter bags can be found online.