Leveraging external data is a topic that have recently received much attention. The propensity score-integrated approaches are a methodological innovation for this purpose. In this paper we adapt these approaches, originally introduced to augment single-arm studies with external data, for the augmentation of both arms of a randomized controlled trial (RCT) with external data. After recapitulating the basic ideas, we provide a step-by-step tutorial of how to implement the propensity score-integrated approaches, from study design to outcome analysis, in the RCT setting in such a way that the study integrity and objectively are maintained. Both the Bayesian (power prior) approach and the frequentist (composite likelihood) approach are included. Some extensions and variations of these approaches are also outlined at the end of this paper.