Answer: You are on the right track with adding organic matter. That is the best addition you can make to build good soil. (If you add sand to clay you will end up with brick when it dries out.) Most vegetables do best on a rich, moist but well drained soil (meaning not soggy) with plenty of organic matter.
If the composted manure is truly well aged it should not burn the plants especially if you work it into the soil. In most cases it also has a substantial amount of straw or shavings mixed with it which also reduces the nitrogen. (The difficulty is in determining the actual analysis of the material because it depends on the animal's diet, the age of the product and how it was composted and whether or not it was covered....)
If your soil is truly poor you might add even more organic matter such as chopped leaves or other less nitrogen-rich material along with it. (Ultimately you will need to run some basic soil tests to judge the results.) For the record, a cubic yard will cover about 160 square feet about two inches thick, so that amount should be fine for your 800 square feet. In fact, you could add up to ten inches of organic matter (other than manure) and it wouldn't be too much! Using an organic mulch during the growing season can also help build your soil as it decays over time, too.
I can't tell you the frost date for your local area, but your County Extension (461-1000) should be able to. They should also be able to help you with the soil tests and interpreting the results, as well.
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