The investigation of RNA-based regulation of cellular processes is becoming an increasingly important part of biological or medical research. For the analysis of this type of data, RNA-related prediction tools are integrated into many pipelines and workflows. In order to correctly apply and tune these programs, the user has to have a precise understanding of their limitations and concepts. Within this manuscript, we provide the mathematical foundations and extract the algorithmic ideas that are core to state-of-the-art RNA structure and RNA-RNA interaction prediction algorithms. To allow the reader to change and adapt the algorithms or to play with different inputs, we provide an open-source web interface to JavaScript implementations and visualizations of each algorithm. The conceptual, teaching-focused presentation enables a high-level survey of the approaches, while providing sufficient details for understanding important concepts. This is boosted by the simple generation and study of examples using the web interface available at http://rna.informatik.uni-freiburg.de/Teaching/. In combination, we provide a valuable resource for teaching, learning, and understanding the discussed prediction tools and thus enable a more informed analysis of RNA-related effects.