Many problems in Information and Data Management require a semantic account of a database schema. At its best, such an account consists of formulas expressing the relationship ("mapping") between the schema and a formal conceptual model or ontology (CM) of the domain. In this paper we describe the underlying principles, algorithms, and a prototype tool that finds such semantic mappings from relational tables to ontologies, when given as input simple correspondences from columns of the tables to datatype properties of classes in an ontology. Although the algorithm presented is necessarily heuristic, we offer formal results showing that the answers returned by the tool are "correct" for relational schemas designed according to standard Entity-Relationship techniques. To evaluate its usefulness and effectiveness, we have applied the tool to a number of public domain schemas and ontologies. Our experience shows that significant effort is saved when using it to build semantic mappings from relational tables to ontologies.