Grid systems offer high computing capabilities that are used in many scientific research fields and thus many applications are submitted to these powerful systems. Parallel applications and applications consisting of interdependent jobs may especially be characterized by a complex workflow. Therefore, Grid systems should be capable of executing and controlling workflow computations. This document sets out our approach to workflow management in a Grid environment. It introduces common steps on how to map an application workflow to the DAG structure, and how to carry out its execution and control. We present the Workflow Management Service (WFMS) implemented and integrated as a part of the CrossGrid project. The purpose of this service is to schedule workflow computations according to user-defined requirements, also providing a set of mechanisms to deal with failures in Grid.