Presented is an introduction to the operation and mechanics of the ACTP production system, a version of Anderson's (1976) ACT system. ACTP is already in use modeling geometry theorem proving and counting of a set of objects, and has been identified as a potentially useful programing framework for developing models of the cognitive processes used in other tasks. The ACTP system is introduced in the context of COUNTER, a model of counting. Section one of this report presents a general overview of the model, including COUNTER's performance on a sample problem, to provide a general idea of how a production system operates. The second section discusses the mechanics of the model, including data structures, schemata, and single productions. The final section follows the sequence of testing and executing productions involved in counting a set of objects. A list of selected references and five appendices are included in this report. (MP)