This article examines effective methods for teaching Comparative Discourse Analysis to university students, with particular attention to developing analytical, critical, intercultural, and research competencies. It argues that successful instruction should move beyond the explanation of theoretical concepts and provide students with systematic experience in analyzing authentic discourse from different linguistic and cultural contexts. Particular emphasis is placed on authentic text analysis, contrastive analytical frameworks, problem-based and collaborative learning, corpus-assisted investigation, close reading, project-based learning, and the appropriate use of digital technologies. The article also highlights the importance of selecting genuinely comparable materials according to genre, topic, communicative purpose, audience, and context. It concludes that the integration of qualitative interpretation with empirical evidence enables students to identify discourse patterns more accurately, justify their interpretations, and conduct increasingly independent comparative research.