Hair algae is a common problem in a reef tank (less so in fish only since copper based medications used in those set ups kill the algae). Here are some ideas:
Definiately use R/O water (as suggested in an earlier reply) going forward for top off and water change. This is the most important first step in fighting the problem. Do as many water changes as you can now and cut down on feeding. Phosphate is a real contributor here, so think about temporary use of a phosphate removal device (sponge, filter, etc.)
Add lots of red legged and left legged hermit crabs and turbo snails to the tank (they will help control any further growth). Stay away from blue legged crabs if you keep snails. They are good on the hair aglae, but like to eat the snails too.
If your tank is large enough (i.e., 75 gallons plus) consider adding a tang (purple, yellow, red sea salfin or Soho tang) - they like hair algae as well.
Cut down on your lighting period until the outbreak is under control.
If you have a UV sterilizer, use it, it will kill any free floating algae (though not the hair algae growing on the rocks/fixtures).
Physically remove as much of the hair algae as you can (i.e., with a siphon during water changes).
If you do all this, you will eventually win the battle (but it will take time).