As artificial intelligence (AI) becomes increasingly integrated into daily life, there is a growing need for users to develop an intuitive understanding of AI, leading to suitable mental models that allow them to understand both potential harms of AI and how to use it responsibly. In the research field of AI literacy, first conceptual models for supporting users in acquiring basic knowledge about AI have been proposed. However, the question of how to implement the proposed competence models and to what extent a given approach enables people to internalize the targeted competences into appropriate mental models of AI has been sparsely addressed so far. This paper presents an experiential learning approach to fostering the AI literacy of users and an exploratory study investigating to what extent the proposed AI competences are internalized by learners and lead to more appropriate mental models of AI. The findings support the suitability of the proposed experiential learning concept for developing a basic form of AI literacy and its effectiveness for supporting the development of appropriate mental models, while providing pointers for future work.