algae needs three things to survive, light, phosphate and nitrates.
nitrates are directly tied to what's in your tank, fish poop and overfeeding are generally the main culprits for this, reduce feeding will help as will a skimmer as mentioned above. running a refugium is another way to absorb these nutrients. there is a cheato reactor build in the DIY section of the forums, really good for people with small spaces. other then that its general maintenance, water/sock changes.
consider getting a gfo reactor, two little fishes do a cheap one. this will help with your phosphate problems. ive also read that you can try turning off your lights for about 3 days to reduce the growth of algae. for 3 days your corals will be fine (so ive read) but im not too sure about it, sure someone will chime in .
if this was my tank, i would physically remove what i can from sand bed and rocks, use a new plastic spoon and take the top layer of where its really stained and do a massive water change. unfortunately water changes are gonna be the main way you export nutrients without the equipment (assuming you dont have them)
hope this helps you and good luck.