Graph deep learning methods have become popular tools to process collections of correlated time series. Unlike traditional multivariate forecasting methods, graph-based predictors leverage pairwise relationships by conditioning forecasts on graphs spanning the time series collection. The conditioning takes the form of architectural inductive biases on the forecasting architecture, resulting in a family of models called spatiotemporal graph neural networks. These biases allow for training global forecasting models on large collections of time series while localizing predictions w.r.t. each element in the set (nodes) by accounting for correlations among them (edges). Recent advances in graph neural networks and deep learning for time series forecasting make the adoption of such processing framework appealing and timely. However, most studies focus on refining existing architectures by exploiting modern deep-learning practices. Conversely, foundational and methodological aspects have not been subject to systematic investigation. To fill this void, this tutorial paper aims to introduce a comprehensive methodological framework formalizing the forecasting problem and providing design principles for graph-based predictors, as well as methods to assess their performance. In addition, together with an overview of the field, we provide design guidelines and best practices, as well as an in-depth discussion of open challenges and future directions.