First we need to discuss what your nutrient levels are and the root cause for the outbreak. Hair algae is fueled by nitrates and phosphates, so we need to get those under control. Most effective way is through water changes with RODI , either a large ...or a series of small ones back to back to get those levels low . (I have no problem changing close to 100% water , other reefers feel this may be too much of a change and do a series of 10 % water changes everyday for a week or more till the numbers show improvement . )
During this time you want to take out any rock that can easily be removed and give it a good scrub using the old tank water and place it back into the aquarium. Scrub , pull at and scrub some more the remaining rock in the aquarium with a toothbrush . Manually remove as much as you can and turn up the flow in the aquarium . Turkey baste the rocks blowing all the crud into the water column . Use a net to capture as much as you can and let the mechanical filter capture the remaining. After the tank clears up , turn the flow back down to normal and change the filter pad or sock . You can do this step as many times during the week as you want to stick your hand in the tank. I just went through this with my new tank and I did it every three days. Get a good clean up crew of various snails , I like the Mexican turbo , they are big hungry eaters . Keep up with those water changes or look into other methods for nutrient control .