Railways are among the most environmentally friendly means of transport, making circulation planning essential for cost-effective and reliable operations. This task involves assigning and sequencing scheduled trips and empty runs for railway vehicles based on given timetables. In the literature, circulation planning problems are represented by several networks, formulated using different models, solved by various methods, and aimed at different objectives. Often, researchers study practical problems from specific partners with a strong focus on the use case. Considering these aspects, this tutorial explains and compares two widely used graph structures and the corresponding mathematical formulations for the fundamental rolling stock circulation planning problem with a homogeneous fleet (i.e., one single type of traction units). A detailed problem description is followed by a comprehensive guideline on how to build a connection-based and a space-time network. We use a real-world case study from Austria and provide 16 instances of different sizes and structures for the basic problem variant online. We assess networks and models in terms of complexity, efficiency, and suitability for extensions. Additionally, we provide managerial insights by evaluating real-world solutions and the trade-off between minimizing traction units and costs from repositioning. This paper contributes to railway fleet management, offering valuable guidance for both theoretical advancements and practical implementations in the field.