This paper presents algorithms that make it possible to process XML data that conforms to XML Schema (XSD) in a mainstream object-oriented programming language. These algorithms are based on our previously developed object-oriented view of the core of XSD. The novelty of this view is that it is intellectually manageable for object-oriented programmers while still capturing the complexity of the core structural properties of XSD. This paper develops two mappings based on this view. The first one is specified by a set of rules that map a source XSD schema into its object-oriented schema. The second one maps XML instances that conform to an XSD schema to their representation as objects. In addition to mapping elements and attributes, these mappings reflect correctly the particle structures including different types of groups, and type derivation by restriction and extension. The structural properties of identity constraints are also mapped correctly. Formally defined mappings or algorithms of this sort have not been available so far, and existing industrial tools typically do not handle the level of complexity of XSD that our mappings do.