What is a web service?

Basically, a web service is an application with which other applications can communicate over via a network, often using XML to encapsulate data and context, and HTTP as the transport layer.

How do we expose a Web Service?

There are several ways (protocols) we can expose our web services to the rest of the world, from a the minimalistic approach of the "RESTafarians", to using XML-RPC, to SOAP and all its accompanying specifications (UDDI, WSDL, WS-Security, WS-Context, etc.)