With strong technology improvement, especially GNSS, coordinate transformation has become an essential tool in everyday practice. For this reason, it is beneficial to have a good understanding of the mathematical process of coordinate transformation, as well as the method for calculating transformation parameters. The purpose of this article is to provide a detailed explanation of the coordinate transformation procedure and the calculation of transformation parameters for seven transformation models: 3-parameter, 5-parameter standard and abridged, 7-parameter, 8-parameter, 9-parameter, and 12-parameter. For each transformation model, a basic transformation equation, a procedure for calculating transformation parameters, inverse expression for reversible transformation, as well as characteristics of each model are provided. As an addition, for each model, a numerical example of calculating transformation parameters for the territory of the Republic of Croatia is provided. Additionally, for the example of the 7-parameter transformation, importance of reversible transformation, rotation convention, as well as the form of the rotation matrix used during transformation are demonstrated.