Federated Learning (FL) stands at the forefront of decentralized machine learning, revolutionizing collaborative model training among distributed devices while maintaining stringent privacy standards. FL requires multiple algorithms to handle issues with model initialization, synchronization, and convergence in remote environments. This paper comprehensively examines FL algorithms, focusing on pivotal techniques such as client-side training, server-side aggregation, and FedAvg. Detailed analysis elucidates these algorithms’ intricate workings, showcasing how they harmonize the aggregation of local model updates with global parameter refinement, thereby striking a delicate equilibrium between privacy preservation and model accuracy. The foundations of FL and the specifics of its sophisticated algorithms are covered in this study. By providing researchers with a roadmap for delving into FL algorithm development, this paper catalyzes unlocking new avenues of innovation and advancing the frontiers of privacy-preserving machine learning. For experimental learning, the federated learning implementation is carried out using the Flower framework on the well-known iris flower classification problem, with performance metrics thoroughly evaluated. Moreover, this paper represents, to our knowledge, the first work that extends the algorithmic directions presented in a review paper with detailed implementation on a sample problem, further encouraging exploration of various algorithms in FL implementation.