The evolution and accessibility of AI technologies have led to extensive use in everyday life, reflecting their usability in teaching and learning. However, the emergence of new tools poses challenges for teachers to select the appropriate ones, as well as for institutions to regulate their use and provide required support. This paper presents a case study by Vytautas Magnus University (Lithuania) that focuses on developing a methodology for university teachers to guide them and provide support when selecting artificial intelligence (AI) tools for teaching and learning. The methodology and support system were created, and feedback from teachers was collected to illustrate the arising challenges and the need for institutional support.