Hidden Markov models play a critical role in the modelling and problem solving of important AI tasks such as speech recognition and natural language processing. However, the students often have difficulty in understanding the essence and applications of Hidden Markov models in the context of a cursory introductory coverage of the subject. In this paper, we describe an empirical approach to explore the subject of the Hidden Markov models. This approach focuses on a series of incremental developments of Hidden Markov models for automatic spelling recognition. The process of programming and experiments with these models cultivates the actual modelling and problem-solving capacity, and guides the students to a better understanding of the application of similar Hidden Markov models used in speech recognition.