Dialectal Arabic (DA) poses a persistent challenge for natural language processing (NLP), as most everyday communication in the Arab world occurs in dialects that diverge significantly from Modern Standard Arabic (MSA). This linguistic divide impedes progress in Arabic machine translation. This paper presents two core contributions to advancing DA-MSA translation for the Levantine, Egyptian, and Gulf dialects, particularly in low-resource and computationally constrained settings: (i) a comprehensive evaluation of training-free prompting techniques, and (ii) the development of a resource-efficient fine-tuning pipeline. Our evaluation of prompting strategies across six large language models (LLMs) found that few-shot prompting consistently outperformed zero-shot, chain-of-thought, and our proposed Ara-TEaR method. Ara-TEaR is designed as a three-stage self-refinement prompting process, targeting frequent meaning-transfer and adaptation errors in DA-MSA translation. In this evaluation, GPT-4o achieved the highest performance across all prompting settings. For fine-tuning LLMs, a quantized Gemma2-9B model achieved a chrF++ score of 49.88, outperforming zero-shot GPT-4o (44.58). Joint multi-dialect trained models outperformed single-dialect counterparts by over 10% chrF++, and 4-bit quantization reduced memory usage by 60% with less than 1% performance loss. The results and insights of our experiments offer a practical blueprint for improving dialectal inclusion in Arabic NLP, showing that high-quality DA-MSA machine translation is achievable even with limited resources and paving the way for more inclusive language technologies.