This tutorial presents an architecture for autonomous robots to generate behavior in joint action tasks. To efficiently interact with another agent in solving a mutual task, a robot should be endowed with cognitive skills such as memory, decision making, action understanding and prediction. The proposed architecture is strongly inspired by our current understanding of the processing principles and the neuronal circuitry underlying these functionalities in the primate brain. As a mathematical framework, we use a coupled system of dynamic neural fields, each representing the basic functionality of neuronal populations in different brain areas. It implements goal-directed behavior in joint action as a continuous process that builds on the interpretation of observed movements in terms of the partner's action goal. We validate the architecture in two experimental paradigms: (1) a joint search task; (2) a reproduction of an observed or inferred end state of a grasping-placing sequence. We also review some of the mathematical results about dynamic neural fields that are important for the implementation work.