One main cause of algae seems to be unhealthy plants. I have used cuttings from algae-plagued tanks when setting up new tanks according to the above suggestions, and have been able to completely eliminate the algae once the plants grew in.
It seems that the worst kinds of algae, filamentous algae and red algae, can thrive even in water that is starved of nutrients when they are attached to a dying leaf (I don't know it derives nutrients from the leaf or what). By having only healthy leaves in the tank, you have already eliminated the favorite breeding ground for these algae.
Presuming you are starting with no-so-healthy cuttings from an unsuccessful tank, so that most of the leaves have firmly attached algae, you must grow out new leaves as quickly as possible so you can eliminate the dying leaves. This is the job of the suggestions presented above. In the mean time, cut off any leaves that are badly covered, and as soon as a stem grows tall, cut it off at the point where the algae starts and replant the top, and discard the bottom. For rosette plants just cut off the infested leaves when sufficient new ones have grown.
For me this has been sufficient to eliminate all algae problems (to the point of no visible algae) when I followed the setup techniques outlined above in some of my tanks. However, this does not eliminate the chance that variations in your tap water chemistry and fish feeding habits will make your job more difficult.
If nitrates read zero, there may be too much light and you can SLOWLY lower the light levels by putting toilet paper or equivalent between the lights and the top glass, while continually removing algae and watching how fast it grows back. More likely to cause algae than either excess nitrates or light are excess phosphates originating from fish food or decaying plant leaves.
At present the only known ways to remove it are with a phosphate removing resin (Phos-Sorb for example) or by water changes. I am currently investigating home-brew alternatives to the expensive Phos-Sorb for algae control based on the ideas in a soil chemistry posting that follows this post immediately.
There is one type of algae that may thrive despite all this advice: blue-green algae. This algae is actually related to bacteria and will respond to treatment with erythromycin, available at most pet shops. Follow the instructions indicated for bacterial infection of fish on the label, but use only half the dosage. The people at the pet shop will think you're crazy for using it on an "algae", but remember that the pet shops are poor sources of information and that blue-green algae is actually a photosynthetic bacteria.
I have used the brand "Maracyn" with success and it has never reappeared. This algae can be identified by the color (usually more bluish than most algae) and the fact that it quickly coats plants/sand in a thin layer like a veil, which is easy to remove from the plant but grows back very quickly. It is not stringy or tufty. This treatment will not harm the filter bacteria if the directions are followed (using 1/2 strength). If you're not sure, get an expert identification before using the medication. Many snails are said to love to eat blue-green algae (e.g. ramshorn and pond snails) and thus provide an organic (but not as quick) remedy.
