Silicon photonic micro-ring resonators (MRR) developed on the silicon-on-insulator (SOI) platform, owing to their high sensitivity and small footprint, show great potential for many chemical and biological sensing applications such as label-free detection in environmental monitoring, biomedical engineering, and food analysis. In this tutorial, we provide the theoretical background and give design guidelines for SOI-based MRR as well as examples of surface functionalization procedures for label-free detection of molecules. After introducing the advantages and perspectives of MRR, fundamentals of MRR are described in detail, followed by an introduction to the fabrication methods, which are based on a complementary metal-oxide semiconductor (CMOS) technology. Optimization of MRR for chemical and biological sensing is provided, with special emphasis on the optimization of waveguide geometry. At this point, the difference between chemical bulk sensing and label-free surface sensing is explained, and definitions like waveguide sensitivity, ring sensitivity, overall sensitivity as well as the limit of detection (LoD) of MRR are introduced. Further, we show and explain chemical bulk sensing of sodium chloride (NaCl) in water and provide a recipe for label-free surface sensing.