The Internet of things (IoT) is transforming the whole of society. It represents the next evolution of the Internet and will significantly improve the ability to gather and analyze data, as well as the ability to control devices remotely. In this respect, the usage of connected devices is continuously growing with the expansion of the applications being offered to individuals and industries. To address IoT market needs, many low-power wide-area (LPWA) technologies have been developed, some operating on licensed frequencies (e.g., narrowband-IoT [NB-IoT] and Long-Term Evolution-M [LTE-M]), and others on unlicensed frequencies (e.g., LoRa, Sigfox, etc.). In this paper, we address the Release 13 of the NB-IoT 3rd generation partnership project (3GPP) standardized LPWA technology and provide a tutorial on its physical layer (PHY) design. Specifically, we focus on the characteristics and the scheduling of downlink and uplink physical channels at the NB-IoT base station side and the user equipment (UE) side. The goal is to help readers easily understand the NB-IoT system without having to read all the 3GPP specifications or the state-of-the-art papers that generally describe the system. To this end, each presented concept is followed by examples and concrete use-cases to further aid in the reader's comprehension. Finally, we briefly describe and highlight the new features added to the NB-IoT system in Releases 14 and 15.