Small Town America: A Narrative History, 1620-The Present, by Richard Lingeman. Boston: Houghton Mifflin Company. 547 pp. $8.95.

How America's ''small town'' values have arisen, flourished, faltered, and survived, along with the towns themselves, is the story Lingeman tells with the zeal of a researcher and the sympathy of a man who left his hometown for the city. The generally pithy prose sometimes gets heavy, overwrought, or nonobjective, but that's a small price to pay for a book that illuminates the meanings of ''community'' - from the days of the Plymouth Colony until now.