Building complex entities like Network Slices and their Subnets requires proper models and methods to allow their convenient design and deployment. Despite significant progress in the standardization of the basic Network Slicing concepts, for many it still remains unclear how to organize a Network Slice/ Subnet design process that would be aligned to the currently standardized, declarative style of their provisioning. How to reflect the high-level, abstract service requirements into a technical description of a Network Slice/Subnet capable of fulfilling them?In what form should such a description be provided? What details should it cover and how to conduct a design process leading to the production of a concretized description of the desired Network Slice Instance (NSI) and/or Network Slice Subnet Instance (NSSI)? Unfortunately, the current standardization scope does not cover these challenging design-time aspects, leaving the telco community without clear guidelines in this complicated area. Also, the state-of-the-art research does not tackle the corresponding challenges in a generic and holistic way. We contribute to fill in this void by complementing the up-to-date standards with original concepts and systematizations compiled into a comprehensive tutorial on the Network Slicing design-time aspects. To this end, we deliver a broad study of the evolution of Network Slice/Subnet provisioning approaches and offering modes, explaining their impact on the design phase. Next, we provide a generic taxonomy of building blocks out of which an NSI/NSSI may be designed, followed by proposing precise definitions of the design process and its expected outcomes. Then, by elaborating on those definitions, we explain, in a technology-agnostic manner, the activities comprising the design process and the results it shall produce. Based on these fundamentals, we describe the opportunities for automating the design process, essential to support the declarative provisioning style and to offer the "dynamic slicing" capabilities by the Slicing orchestrators. All of the elaborated systematizations and concepts are vendor-agnostic and fully standards-aligned which makes them practically usable in a wide range of solutions.