Augmented reality entails the use of models and their associated renderings to supplement information in a real scene. In order for this information to be relevant or meaningful, the models must be positioned and displayed in such a way that they blend into the real world in terms of alignments, perspectives, illuminations, etc. For practical reasons the information necessary to obtain this realistic blending cannot be know a priori, and cannot be hard-wired into a system. Instead a number of calibration procedures are necessary so that the location and parameters of each of the system components are known. In this paper we identify the calibration steps necessary to build a computer model of the real world and then, using the monitor-based augmented reality system developed at ECRC (Grasp) as an example, we describe each of the calibration processes. These processes determine the internal parameters of our imaging devices (scan converter, frame grabber, and video camera), as well as the geometric transformations that relate all of the physical objects of the system to a known world coordinate system.