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The Ptolemy project studies modeling, simulation, and design of concurrent, real-time, embedded systems. The focus is on assembly of concurrent components. The key underlying principle in the project is the use of well-defined models of computation that govern the interaction between components. A major problem area being addressed is the use of heterogeneous mixtures of models of computation. Ptolemy II takes a component view of design, in that models are constructed as a set of interacting components. A model of computation governs the semantics of the interaction, and thus imposes an execution-time discipline. Ptolemy II has implementations of many models of computation including Synchronous Data Flow, Kahn Process Networks, Discrete Event, Continuous Time, Synchronous/Reactive and Modal Model. This hands-on tutorial explores how these models of computation are implemented in Ptolemy II and how to create new models of computation such as a "non-dogmatic" Process Networks example and a left-to-right execution policy example.