Dinos can be no big deal, or they can be one of the worst things that ever happen to your tank. I had an outbreak that started after a major reaquascaping last summer, and I never could get on top of them - I lost all my corals and now have a friend keeping my fish while I restart the system from scratch.
First thing I'd suggest you do is contact Pants, get him a sample of your dinos and have him ID them for you. His website (www.algaeid.com) can be helpful but it's a better idea to put them under a microscope. Once you know what you're dealing with, you'll have a slightly better chance of combating them.
But only slightly better. As treesprite said, the prevailing theory right now is that dino blooms occur in the low nutrient range where macroalgae and filamentous algae can't survive. Slightly higher nutrient levels allow those algae to outcompete dinos, but down in the low ppm range the dinos can grow out of control. Personally, I also think there's a link between certain species of dinos and the types of bacteria in the system as they've been shown to have a near-symbiotic relationship, and some people have had success with approaches that affect bacteria growth. But there's not much definitive info in this area - certainly not enough for carbon dosing, bacterial supplements or antibiotics to be considered a reliable approach to eradication.
There are a couple of recent threads on ReefCentral about them. One thread mainly concerns hydrogen peroxide dosing and the other is more broad in scope. From what I've read (and believe me, I've read a lot), there are people who've had success with every method out there, but for every person who found a way to beat them there are even more for whom that particular method had no effect at all.
For what it's worth, I had a strain of Ostreopsis in my system (see the attached image and also this link). I tried dosing hydrogen peroxide. I tried Fauna Marin Ultra Algae-X. I tried setting up an algae scrubber. I tried manual removal with aggressive mechanical filtration. I tried extended lights-out periods and big water changes. I tried running reactors full of Purigen and Cuprisorb. Many of these were initially promising (especially in combination with lights off) but eventually the dinos would always come back. The only thing I didn't try was letting them run their course - maybe they'd have eventually consumed whatever was sustaining them and then died back.
But let me tell you, when Ostreopsis dies off, it releases a palytoxin which is none too good for the humans in your house. It was so bad while I was running Algae-X that an hour in my basement would bother my eyes to the point that I couldn't see well. Finally I got sick of the whole thing and just nuked my tank - 40 gallons of chlorine bleach right into the main tank, with a separate acid bath for the rock. Right now I'm waiting to do a few mods to my system before refilling it with water again.
So be patient, be observant, be diligent. You may be able to beat them, or you may not. All I can say is good luck.