In order to effectively provide ultra reliable low latency communications and pervasive connectivity for Internet of Things (IoT) devices, next-generation wireless networks can leverage intelligent, data-driven functions enabled by the integration of machine learning (ML) notions across the wireless core and edge infrastructure. In this context, this paper provides a comprehensive tutorial that overviews how artificial neural networks (ANNs)-based ML algorithms can be employed for solving various wireless networking problems. For this purpose, we first present a detailed overview of a number of key types of ANNs that include recurrent, spiking, and deep neural networks, that are pertinent to wireless networking applications. For each type of ANN, we present the basic architecture as well as specific examples that are particularly important and relevant wireless network design. Such ANN examples include echo state networks, liquid state machine, and long short term memory. Then, we provide an in-depth overview on the variety of wireless communication problems that can be addressed using ANNs, ranging from communication using unmanned aerial vehicles to virtual reality applications over wireless networks as well as edge computing and caching. For each individual application, we present the main motivation for using ANNs along with the associated challenges while we also provide a detailed example for a use case scenario and outline future works that can be addressed using ANNs. In a nutshell, this paper constitutes the first holistic tutorial on the development of ANN-based ML techniques tailored to the needs of future wireless networks.