The rapid expansion of spiking neural networks (SNNs) has led to a proliferation of training algorithms that differ widely in biological inspiration, computational structure, and hardware suitability. Despite this progress, the field lacks a unified, fine-grained taxonomy that systematically organizes these approaches and clarifies their conceptual relationships. This survey provides a comprehensive taxonomy of SNN training algorithms, spanning surrogate-gradient backpropagation, local and three-factor learning rules, biologically inspired plasticity mechanisms, ANN-to-SNN conversion pipelines, and non-standard optimization strategies. We analyze each class in terms of its computational principles, learning signals, and locality properties. To support reproducible research, we release NeuroTrain, an open-source snnTorch-based framework that implements a representative set of these algorithms within a unified, modular, and extendable framework, enabling consistent benchmarking across datasets, architectures, and training regimes. By consolidating fragmented literature and providing a reusable benchmarking framework, this survey identifies common patterns, highlights open challenges, and outlines promising directions for future work on scalable, efficient SNN training.