First thing to do is remove as much as you can by hand. I usually twirl it around a barbecue skewer and pull gently until I get a good wad of it, like getting cotton candy onto a cone. Keep doing that until you can't find any more clumps.
Next, do a water change to reduce available nutrients in the water column. If you use plant nutrients heavily or tend to overfeed like I do, 50%+ is a good place to start when it comes to starving out hair algae. Keep doing water changes on a regular basis (I shoot for 10-25% every week, but in reality it's usually every two or three weeks) to keep the overabundance of nutrients in check.
You can spot-dose store bought hydrogen peroxide (the regular 3% kind) with a dropper onto remaining patches of algae; they should start to die off immediately and change color to red or brown. Those bits can then be pulled out or siphoned up. Used in small amounts (like a couple droppers' worth, not a quarter bottle), peroxide shouldn't hurt anything in your tank and will quickly break down to water and oxygen.
After those initial steps, keeping control of hair algae involves getting your plants to outcompete it for food. One really easy way to do that is to add more plants and keep using the same amount of fertilizer. You'll know when to increase your dose when the plants start looking like they're deficient or not growing as well as before; make small changes and wait at least a few days to see how they respond.
Aside from more plants, a nerite snail is a great addition to your cleanup crew. I've never had one try to escape before, but a female nerite will lay eggs on your hardscape. They're small and white and look like sesame seeds. The eggs won't hatch in fresh water or harm your tank.
Good luck! I know hair algae is a hassle and hope this works for you.