Harv,
From your comments I presume that your water clarity problems are not due to suspended silt, but rather to algal blooms. However, I will give you some ideas on both.
Most ponds that stay muddy all of the time have large populations of common carp, buffalo, or bullhead catfish stirring up the bottom, looking for food. The appropriate action here is renovation, either by draining the pond completely, or by eradicating the fish using a chemical called rotenone. Rotenone inhibits a fish's ability to absorb oxygen through the gills, causing death. It must be applied by a licensed applicator.
If these species aren't present, then the muddiness is due to soil type and runoff. Certain types of clay suspend in the water indefinitely. These ponds can be cleared using hay or agricultural gypsum. Break up two bales of good dry hay per surface acre and scatter on the pond every two weeks. for a maximum of 4 applications per year. Don't use more, or the decaying hay may rob the pond of oxygen and kill your fish. Agricultural gypsum should be applied at a rate of approximately 500 lbs per acre/foot of water to clear a muddy pond. To determine how many acre/feet you have in your pond, take the total acreage and multiply by the average depth. For example, if Harv's pond is 2 acres, and averages 7 feet deep, that would be 14 acre/feet (i.e. the water in his pond would cover 14 acres with one foot of water). The next year, considerably less gypsum will be needed, perhaps 10% of the original amount if all goes well.
Vegetation or algal blooms are a different matter. Algae is what gives the pond its green cast. In cases of excess nutrient input, filamentous algae can appear. Algae is not rooted to the bottom, nor does it have leaves, but other submerged plants are often referred to as "algae". The first thing to address is the source of nutrients, if algal growth is excessive. If there are livestock in your pond's watershed, a buffer strip between them and the pond will help tie up some of the nutrients. If no source can be identified, or the source can't be eliminated, you have to treat the pond. There are two possible methods, chemicals or dyes.
The best chemical to reduce algae is copper sulfate, sold at co-ops under the "Bluestone" trademark among others. Apply 2 lbs per surface acre (NOT per acre/foot; e.g. Harv would need 4 lbs). There are no usage restrictions (livestock watering, etc.), and the compound quickly becomes inert. This is the safest aquatic herbicide around, in my opinion. One caution, treat no more than half of the pond at any one time, because the decaying vegetation uses up oxygen. Finish the treatment in 1-2 weeks.
Many dyes are available to reduce sunlight penetration and eliminate algal growth. You can dye your pond whatever color you want. Aquashade is a common one, and can be found at the co-op. The downside to this is that more than one application is needed per year, and it is kind of expensive.
Algae is the first link on the food chain, so reducing or eliminating it will reduce the numbers and growth of any fish in the pond. For many people, that is an acceptable trade-off, because they can use the pond for other forms of recreation.
Hope this information helps. Probably more than you wanted to know.