Great advice, from the FL&UL host <img src="/images/graemlins/smile.gif" alt="" />
Generally, algaes love to bloom when nutrients are plentiful in the tank; specifically nitrates and phosphates (in the fishtank, the large majority of these compounds come from fish waste and any decomposition of food scraps/dying plants). Lighting is of course another stimulator, but unlike other aquatic plants, algaes grow even under minimal lighting. For unicellular algae problems, limiting feeding, more frequent water changes, and using products which "soak up" excess nutrients (phosphate sponges or Purigen bio-beads, for instance) are usually enough to control spread (I do not recommend use of algacides, which may interfere with biofiltration)
In your case though, hair algae is even more tricky and needs really aggressive treatment... meaning you need to manually cut and remove as much as you can find. This stuff is very tenaceous and difficult to get rid of once it takes off, so catching it early is key. It may even mean pruning a lot of leaves if you have live plants. Over time, more frequent water changes and watching stocking levels of the tank will improve it just as with other algaes, but this is not a quick process. For really extreme cases where nothing seems to help, careful soaks of objects in a separate bin of bleach (followed by a wash in clean water afterwards to remove residue) will do the trick (this must be done quickly for live plants to avoid killing them).
Here are some other tips from the Algae FAQ at TheKrib.com:Hair (thread) Algae