Reservoir Computing (RC) is a promising approach for time-series forecasting that offers efficient and sustainable deep learning alternatives to traditional neural networks. This tutorial provides an introduction to sustainable deep learning with RC, including its theoretical foundations, practical implementation, and advantages over other approaches. The tutorial starts with an overview of the RC framework, including the Echo State Network (ESN) and Liquid State Machine (LSM) models. The fundamental principles of these models are explored, including their unique network structure, the learning mechanisms, and the fundamentals of RC mathematical background. The tutorial then proceeds to explore the strong links with computational neuroscience, and the exciting recent advances in neuromorphic hardware implementations of reservoirs. Finally, the tutorial covers practical implementation aspects, existing software libraries, as well as successful application examples in several domains including automotive, avionics, health, and robotics. In addition to providing practical guidance, this tutorial also emphasizes the importance of sustainability in deep learning. The environmental impact of training deep neural networks is substantial, and RC offers a more energy-efficient approach that is particularly well-suited for time-series forecasting. By using RC, researchers can reduce the carbon footprint of their research while achieving state-of-the-art results. Overall, this tutorial provides a comprehensive introduction to sustainable deep learning with RC for time-series forecasting, and it is suitable for both beginners and advanced researchers looking to explore this exciting area of machine learning.