The proliferation of Large Language Models (LLMs) has revolutionized the field of Natural Language Processing (NLP), yet their benefits remain largely concentrated in high-resource languages like English. This chapter addresses the critical challenge of applying LLMs to low-resource languages, which lack the extensive digital data required for traditional model training. We explore the efficacy of zero-shot and fewshot learning as powerful, data-efficient paradigms for unlocking the capabilities of LLMs in these under-served linguistic contexts. This chapter provides a comprehensive overview of the theoretical underpinnings of zero-shot and few-shot learning, followed by a detailed review of the current state-of-the-art. We propose a structured methodology centered on advanced prompt engineering techniques to maximize performance on a variety of NLP tasks, including translation, sentiment analysis, and named entity recognition. Through a series of experiments on several low-resource African languages (Swahili, Yoruba, Hausa, Zulu, and Amharic) using benchmark datasets like FLORES-200, we demonstrate that few-shot learning significantly outperforms zero-shot approaches and, in some cases, can approach the performance of fully supervised models without the need for extensive labeled data. The results highlight the critical role of in-context learning and prompt design in bridging the performance gap. This chapter concludes with a discussion of the practical implications, current limitations, and future directions for creating more equitable and inclusive language technologies.