Today one of the biggest problems found in developing and implementing Artificial Neural Networks (ANN) is the lack of a rigorous methodology that ensures the development of optimum ANN, because the performance of their function is measured by trial and error, leading to loss of time in training networks that are far away to reach the expected error rate and adequate performance. As a part of the investigation, a method for determining the optimal networks for prediction and function approximation networks with more than one output is proposed and developed. However, steps can be implemented in hard systems methodologies to analyze the characteristics of the variables required for training the ANN and the correlation between them to reduce the optimal search time. A methodology for the construction and development of an ANN is proposed and developed based on Checkland, Jenkins and Hall methodologies, obtaining a 14-step methodology grouped into three stages.