Chlorine tablets that sit against the the pool plaster can cause yellow or black stains. If you use an algaecide with copper in it, the tablet can leach oxidized copper from the water and leave a black stain on the plaster. Because chlorine compounds in the tablets are powerful chemicals, they may also leach other chemicals out of the water and leave stains around the tablets in the plaster.
Drain the pool to expose the stained surface. As the water drops, scrub the sides of the pool with a pool brush to loosen any dirt, algae or debris. When the pool is empty, clean it thoroughly to prepare for the acid wash.
Put on protective clothing, rubber boots, rubber gloves, goggles and a breathing mask. Don't just use a filter. Concentrated acid fumes are highly toxic, can cause lung damage and will penetrate a simple filter. Use a breathing mask with an external air supply.
Mix 1 gallon of acid to 1 gallon of water in a watering can like you use to water flowers. Do not add water to the acid to prevent undiluted acid from splashing on you. Spray the stained area with a water hose to wet the surface. As long as you're going to all this trouble, you should go ahead and do the whole pool. The acid will remove a thin layer of plaster from the pool surface. Don't acid-wash very often or you'll need to replaster the pool.
Sprinkle the acid mixture on the stained area and on a 10-foot section around it. Start at the top and sprinkle the surface down to the bottom in a 10-foot wide section. Wait no more than 30 seconds.
Scrub the stained area and the rest of the acid-washed area with the acid brush to move the acid and dissolved plaster around. You may have to use a little more acid wash on badly stained areas. Rinse quickly with the water hose. Don't put a sprayer on the nozzle -- just let it run softly so it doesn't splash acid around. Rinse quickly and thoroughly until the acid is washed completely away. Repeat the process on the next 10-foot wide section of the pool wall and floor.
Repeat the acid wash if the stains are not removed. For the chlorine tablet stains you might have to increase the acidity of the mixture by 2 parts acid to 1 part water. Be very careful to rinse the acid down into the very bottom of the pool. The rinse water will dilute the acid enough to prevent it from etching a channel in the bottom of the pool. Try not to acid-wash the entire pool more than twice in one go to prevent burning the plaster.
Add soda ash by broadcasting it over the water in the bottom of the pool to neutralize the acid. Stir it by scrubbing the bottom with the pool brush. Use the portable pump to pump out the neutralized acid water from the bottom of the pool. Be careful where you pump the water. Even if you neutralize it properly it can kill plants and animals. Rinse the bottom of the pool again and pump it out. Be sure to clean thoroughly around the drain.
Refill the pool with water and reset the pH and chlorine levels.