Commonly constructed before World War II dug wells are no longer typically constructed. Because of associated contamination issues and the intense effort involved in constructing a dug well they have been replaced with bored wells.
Dug wells were lined with bricks or stones (as seen in the image below) and a wood, stone, or concrete cover was placed over the well. (Image courtesy Glynn Beck, Kentucky Geological Survey)
Dug Well Image
There are some distinct problems with using dug wells that have made them obsolete. First is the problem with the depth of the well. Dug wells are typically only a few feet deeper than the water table and if there is a dry period, let alone a drought, the well can dry up. Second is the way dug wells are constructed.  The walls are there more to keep the well from collapsing in on itself rather than to keep surface water out.  Because of this type of construction, dug wells are highly susceptible to surface water and bacteria contamination.