The integration of Generative Artificial Intelligence (GenAI) into education has the potential to revolutionize teaching methods by providing individualized, inclusive, and successful learning experiences. This study intends to create a comprehensive framework for the effective use of GenAI in education. The proposed framework focuses on prompt engineering discussing the main components for an effective prompt, hence improving teaching excellence across a variety of educational topics. The study focuses on developing practical case studies including ready-to-use prompts to assist university professors and instructional designers in using GenAI into their teaching practices.