Clay soil is too dense and does not allow the plant roots to breath. It also does not drain well causing root rot.
Sandy soils lose water too quickly and are low in nutrients.
If you are stuck with these soil types in your vegetable garden, its time to start improving soil structure before you plant this year. Vegetable plants thrive in a loose, well drained, sandy loam. Till or spade in the material to a depth of 8 to 10 inches. Make sure your garden soil is workable and not too wet. Tilling wet soil will compact it and destroy the soil structure.