The bleach method is to get rid of various species of hair algae that are not eaten by snails or fish and don't seem inclined to go away on their own when you try various management methods---more nutrients, fewer nutrients, more plants, blackout methods, excel overdosing, H2O2 dosing, etc. The purpose is to eliminate the offending algae entirely. Some of the worst hair algae that often require resorting to the bleach method are Cladophora, Rhizoclonium and Oedogonium. These hair algae species get introduced with a new plant or a new fish. They do not form spores that are resistant to bleach.
For the bleach treatment to be effective, the plants have to be treated with diluted bleach and then put in a new aquarium that is free of hair algae. If you treat them and then put them back in the aquarium they came from, the hair algae will just climb back on them and you will have accomplished exactly nothing. Bleach---sodium hypochlorite---is an oxidizing agent, and it is effective only if it kills the hair algae that is attached to a plant without killing the plant. However, the treatment will injure most aquarium plants to some degree. In almost all cases, if given good care after treatment, the injured plant can recover.
First you must set up a new aquarium and get it ready to receive the bleached plants. It must be free of hair algae. Gravel, tank and tank paraphernalia may have to be sterilized if there has been hair algae in the tank. To do this treat the gravel with a 10% bleach solution for 10 to 20 minutes and then rinse well. Fill up the tank with tap water, add paraphernalia, and add about 1 cup of bleach per 10 gallons. Let the tank stand with a glass cover for a day or two, then drain and rinse. When everything has been bleached and rinsed, you can put in the gravel, water, etc. and let it stand for a day or two while any residual bleach escapes or is neutralized. Soil from anywhere except near a lake or a pond will be free of the bad kinds of hair algae, and so you can put soil under the gravel without worrying about introducing hair algae. If you put a couple of pieces of dry dog food or cat food in a dish of water that also has a spoon full of soil and let bacteria grow for two days and then pour the contents into the aquarium the organic matter introduced will neutralize any residual bleach, tie up heavy metals in the water, and make the water ready for introducing fish. The bacteria introduced will include bacteria that oxidize ammonia to nitrate, thus greatly speeding the cycling of the tank. If fish are introduced from a tank that has hair algae, they should spend a day in a "rinse" tank so that any hair algae carried along with them will fall down into the gravel and not be likely to be carried with the fish when they are netted out of the rinse tank and carried (with a clean net) to the hair algae free tank. I usually do not introduce fish into the hair algae free tank, but rather Daphnia and snails to control green water and the soft attached forms of algae that snails like to eat.
Bleaching the plants is done with liquid bleach diluted to 5% (1 part of liquid bleach plus 19 parts water), and the object is to kill all the hair algae on the plant without killing the plant. Thin-stemmed plants can usually take 2 to 3 minutes in the 5% bleach, and thicker stemmed plants, and crown plants or plants with thick rhizomes, like Cryptocoryne or Anubias can take 4 minutes or longer. The toughest hair algae is Cladophora, which requires 4 minutes to kill it completely. Fortunately, Cladophora does not spread rapidly and is found attached to the bases of plants and the older parts of plants and not to the newer parts of thin-stemmed plants. The tough, old plants, crown plants, etc, where Cladophora is attached can easily survive the 4 minute treatment. Rhizoclonium, Oedogonium, black beard algae, staghorn algae and other types are more sensitive, and can be killed by two to three minutes exposure. Even mosses can be cleared of hair algae (except Cladophora) without killing them. It is fortunate that so many types of hair algae are so sensitive to bleach.
After the treatment it is important that the plants be immediately put into a well-lit tank with good growing conditions. If left in a jar of water in dim light or in a pan for a day or two they go down hill quickly and die. Even untreated plants don't last long under those conditions.
Once a planted tank is free of hair algae, it almost always stays free of hair algae for years. Hair algae can be introduced with a new fish or a new plant. New fish should be put in the "rinse" tank first, and new plants should always be bleached.
It works for me!