The climate system is intricate, involving numerous interactions among various components at multiple spatio-temporal scales. This complexity poses a significant challenge in understanding and predicting weather extremes within the Earth's climate system. However, a better understanding of the dynamics of such events is crucial due to their profound impact on ecosystems, economies, and worldwide communities. This tutorial will offer a comprehensive guide on using Regime-PCMCI (Saggioro et al., 2020), a constraint-based causal discovery technique, to uncover the causal relationships governing anomalous climate phenomena. Regime-PCMCI is designed to uncover causal relationships in time-series where transitions between regimes exist, and different causal relationships may govern each regime. In this tutorial, we will first discuss how to frame the problem of understanding climate and weather extremes using regime-specific causal discovery. We will shortly introduce constraint-based causal discovery and present the Regime-PCMCI algorithm. To enable participants to gain hands-on experience with the algorithm, we will apply Regime-PCMCI, implemented in the open-source Python package Tigramite (https://github.com/jakobrunge/tigramite), to a real-world climate science problem. Our example will focus on validating hypothesized regime-specific causal graphs that describe the causal relationship between atmospheric circulation, temperature, rainfall, evaporation, and soil moisture under various moisture regimes. Our tutorial will cover essential steps such as data preprocessing, parameter selection, and interpretation of results, ensuring that all participants with a basic understanding of climate science or data analysis can grasp the presented concepts. With this tutorial, we wish to equip participants with the skills to apply Regime-PCMCI in their research to further uncover complex mechanisms in climate science, as this knowledge is crucial for more informed policy-making.