Cyanobacteria is classified as a photosynthetic organism with properties of both algae and bacteria. Usually referred to as red slime algae in the hobby, cyanobacteria can actually range in color from red and purple to black and even a brilliant green. Cyanobacteria benefits from aquarium lighting, uneaten fish food and poor aquarium maintenance habits. Once the slime spreads, it can quickly carpet your coral, substrate, live rock and even your aquarium glass or acrylic.
Cyanobacteria appears when high nutrients (phosphates, nitrates and silicate) are combined with certain light, temperature and water flow conditions.
The first thing you want to do is test your aquarium water. Nitrate and phosphate levels are generally elevated when cyanobacteria is present.
Perform frequent water changes using nitrate and phosphate-free saltwater to get your tank parameters back in check. A general recommend changing 10-15% of your total tank volume once per week. It is of utmost importance that the freshwater you use to mix your saltwater and top off your aquarium is also free of nitrates, phosphates and silicates.
Cyanobacteria thrives in lower flow environments. Your filtration system should be turning over 8 to 10 times your total tank volume per hour to help keep the water clean. Positioning your powerhead, even adding another, to increase the flow through problematic areas (aka "dead spots") will also help combat the problem. If your aquascape is stacked into a wall without any gaps, caves or crevices for water to circulate, you may eventually want to consider rearranging your rockwork into something more open. Routinely check your protein skimmer to ensure it is operating efficiently and clean out your collection cup at least once each week.
Old light bulbs and/or improper light spectrum can also contribute to cyanobacteria and nuisance algae growth. Take note when you replace your bulbs so you can set a reminder on your phone or calendar to change them out again in 6-18 months (excluding LEDs). Avoiding heavy warm colors, like red and yellow, may help some.
This will probably be easier if you have a controller or monitoring device, but check to see what is the average temperature of your aquarium. Stability is essential and many hobbyists have reported accelerated growth in tanks where temperatures are above 80°. If appropriate for the livestock in your tank, keeping the water temperature 76° to 78° is a small adjustment that can make a big difference.