Cloud computing is becoming an increasingly lucrative branch of the existing information and communication technologies (ICT). Enabling a debate about cloud usage scenarios can help with attracting new customers, sharing best-practices, and designing new cloud services. In contrast to previous approaches, which have attempted mainly to formalize the common service delivery models (i.e., Infrastructure-as-a-Service, Platform-as-a-Service, and Software-as-a-Service), in this work, we propose a formalism for describing common cloud usage scenarios referred to as cloud usage patterns. Our formalism takes a structuralist approach allowing decomposition of a cloud usage scenario into elements corresponding to the common cloud service delivery models. Furthermore, our formalism considers several cloud usage patterns that have recently emerged, such as hybrid services and value chains in which mediators are involved, also referred to as value chains with mediators. We propose a simple yet expressive textual and visual language for our formalism, and we show how it can be used in practice for describing a variety of real-world cloud usage scenarios. The scenarios for which we demonstrate our formalism include resource provisioning of global providers of infrastructure and/or platform resources, online social networking services, user-data processing services, online customer and ticketing services, online asset management and banking applications, CRM (Customer Relationship Management) applications, and online social gaming applications.