There are a lot of products which will kill algae. The ones allowed around fish will dramatically increase the nutrients in the water as the algae rots - unless we get it out quickly, usually through frequent partial (or in real emergencies complete) water changes.

Some herbicides will kill the fish too and sellers suggest removing the fish. I imagine that either the poison breaks down or one must get all of the water out and wash down the pond. If that was the case, I might just break the pond down, remove everything possible, maybe bleach and start over.

The accumulation of nutrients and the additional collection of leaves over the fall, winter and early spring is why many pond keepers break down the pond every spring, clean it out very well and start over. It is like the entropic park lake which is drained because it is beyond help in most any other way. We see that in aquariums too. A complete die off in an aquarium (or pond or even in a lake with insufficient outflow) may occur because we let this process of accumulating nutrients and waste products go on too long.

There is a tendency of water in streams in the beginning (headwaters) of a river system to start as low nutrient, often highly oxygenated, oligotrophic water. Fish and insect populations are low, but this is where trout will live in some mountain areas. Going down stream in a river from the headwaters one can find a mesotrophic zone.

In that zone, the waters are more productive, but many of the invertebrates and fishes and even plants will be different. It will generally be more more productive and the fish population will be of a greater density. That zone may even be more productive in cold and hot weather than the more nutrient rich entropic zone.

The Eutoropic zone will often be more productive per square whatever than the upstream zones and even lake. But again the fauna and flora will change in the proportion of certain species. Some will disappear entirely.

A lot of lakes, rivers and ponds have become entropic because of sewerage plant (sometimes septic tank) releases or other pollutants. Others get a lot of farm or lawn run off, which includes a considerable amount of fertilizer of one sort or another.

I break down all of our aquatic "container gardens" or tubs every fall. Some may be reestablished indoors. Even the Daphnia cultures get drained 80-90%. A lot of the leaf litter, which is the source of so much food for the Daphnia, is pulled out. Those cultures are not very productive in early spring. Part of that is temperature related. As the weather warms up, productivity in the food cultures greatly increases (like right now). I'm actually putting food items in there for the Daphnia, because they are using up all of the plant material and bacteria produced by decaying tree leaves. Biomass in the form of the Daphnia, other tiny crustaceans and small mosquitoes is removed. Partial water changes are also made so that the accumulated "stuff" doesn't increase too much. Really the feeding and water changes are about the same as with an aquarium.

By the way, several crustaceans leave resting eggs in those container bottoms (sort of like brine shrimp eggs in salt lakes.) In a number of cases we do get a spring bloom of brush algae. Shortly there after there is a bloom of seed shrimp or Ostrocods. The algae disappears and I feed Ostrocods like crazy to the fish. I have tried them indoors in fish-less tanks with hair algae and they haven't worked out. <sigh>

A pond is much more sophisticated than my little tubs. (Remember I'm not a ponder and may be leaving some important things out here.) Shading from the sun in the form of water lilies, other floating plants, and even physical structures build over the pond limits sunlight and some algae growth. A large number of "higher plants" absorb a lot of the nutrients. Many "ponders" add larger biofilters. As you know the biofilters biologically break down the more toxic waste materials (ammonia, nitrites) into less toxic waste materials (nitrates). These still need to be removed through a denitrification system (either items which will absorb the nitrates or maybe some sort of wet-dry filter). Partial water changes in many cases still need to be made.

http://saltaquarium.about.com/od/denitratorunits/Natural_Nitrate_Reduction_NNR_Filtration_Methods.htm

So using one or several approaches your mom is going to have to get rid of a lot of the nutrients in the pond. Even algae eating fish can create a problem if their waste isn't removed since it just adds ammonia to the water. (Ask many "pleco" owners about this.)

So the bottom line very likely may include water changes. A small sump pump or large power head may be used to pump water out, so long as measures are made so that the goldfish do not get sucked in. If the pond is at the top of a hill or is out of the ground, siphons of course may be used. Maybe ideally that stuff gets sent to a garden.