Access to external information is an important need for Answer Set Programming (ASP), which is a booming declarative problem solving approach these days. External access not only includes data in different formats, but more general also the results of computations, and possibly in a two-way information exchange. Providing such access is a major challenge, and in particular if it should be supported at a generic level, both regarding the semantics and efficient computation. In this article, we consider problem solving with ASP under external information access using the DLVHEX system. The latter facilitates this access through special external atoms, which are two-way API style interfaces between the rules of the program and an external source. The DLVHEX system has a flexible plugin architecture that allows one to use multiple predefined and user-defined external atoms which can be implemented, e.g., in Python or C++. We consider how to solve problems using the ASP paradigm, and specifically discuss how to use external atoms in this context, illustrated by examples. As a showcase, we demonstrate the development of a HEX program for a concrete real-world problem using Semantic Web technologies, and discuss specifics of the implementation process.