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Science and engineering applications are now generating data at an unprecedented rate. From large facilities such as the Large Hadron Collider to portable DNA sequencing devices, these instruments can produce hundreds of terabytes in short periods of time. Researchers and other professionals rely on networks to transfer data between sensing locations, instruments, data storage devices, and computing systems. While general-purpose networks, also referred to as enterprise networks, are capable of transporting basic data, such as e-mails and Web content, they face numerous challenges when transferring terabyte- and petabyte-scale data. At best, transfers of science data on these networks may last days or even weeks. In response to this challenge, the Science Demilitarized Zone (Science DMZ) has been proposed. The Science DMZ is a network or a portion of a network designed to facilitate the transfer of big science data. The main elements of the Science DMZ include: 1) specialized end devices, referred to as data transfer nodes (DTNs), built for sending/receiving data at a high speed over wide area networks; 2) high-throughput, friction-free paths connecting DTNs, instruments, storage devices, and computing systems; 3) performance measurement devices to monitor end-to-end paths over multiple domains; and 4) security policies and enforcement mechanisms tailored for high-performance environments. Despite the increasingly important role of Science DMZs, the literature is still missing a guideline to provide researchers and other professionals with the knowledge to broaden the understanding and development of Science DMZs. This paper addresses this gap by presenting a comprehensive tutorial on Science DMZs. The tutorial reviews fundamental network concepts that have a large impact on Science DMZs, such as router architecture, TCP attributes, and operational security. Then, the tutorial delves into protocols and devices at different layers, from the physical cyberinfrastructure to application-layer tools and security appliances, that must be carefully considered for the optimal operation of Science DMZs. This paper also contrasts Science DMZs with general-purpose networks, and presents empirical results and use cases applicable to current and future Science DMZs.