Generative Artificial Intelligence (GenAI) tools such as ChatGPT are emerging as a revolutionary tool in education that brings both positive aspects and challenges for educators and students, reshaping how learning and teaching are approached. This study aims to identify and evaluate the key competencies students need to engage with GenAI in education effectively and to provide strategies for lecturers to integrate GenAI into teaching practices. The study applied a mixed-method approach with a combination of a literature review and a quantitative survey involving 130 students from South Asia and Europe to obtain its findings. The literature review identified 14 essential student skills for GenAI engagement, with AI literacy, critical thinking, and ethical AI practices emerging as the most critical. The student survey revealed gaps in bias awareness, and handling unexpected and incorrect AI output. In our study of lecturer strategies, we identified six key areas, with Integration and Curriculum Design being the most emphasized. This highlights the importance of incorporating GenAI into education. While literature prioritized ethics and policy development, students favour hands-on, project-based learning and practical AI applications. To foster inclusive and responsible GenAI adoption, institutions should ensure equitable access to GenAI tools, establish clear academic integrity policies, and advocate for global GenAI research initiatives.