Graph representation learning has become central to many graph-based tasks, driving advancements in various domains such as web search, recommendation systems, and social network analysis. Traditionally, these methods rely on end-to-end supervised learning paradigms that require abundant labeled data, which can be costly and difficult to obtain. To address this limitation, few-shot learning on graphs has emerged as a promising approach, allowing models to generalize with minimal supervision and overcome data scarcity in real-world applications. This tutorial offers an in-depth exploration of recent advancements in few-shot learning for graphs, providing a comparative analysis of state-of-the-art methods and identifying future research directions. We categorize these approaches into two main taxonomies: (1) a problem taxonomy that examines various types of data scarcity problems and their applications, and (2) a technique taxonomy that outlines key strategies for tackling these challenges, including meta-learning, pre-training methods from both the pre-LLM and LLM eras. The tutorial will conclude by summarizing key insights from the literature and discussing future avenues for research, aiming to equip participants with a deep understanding of few-shot learning on graphs and inspire innovation in this rapidly growing field.