Skill extraction is a critical component of modern recruitment systems, enabling efficient job matching, personalized recommendations, and labor market analysis. Despite Türkiye's significant role in the global workforce, Turkish, a morphologically complex language, lacks both a skill taxonomy and a dedicated skill extraction dataset, resulting in underexplored research in skill extraction for Turkish. This article seeks the answers to three research questions: 1) How can skill extraction be effectively performed for this language, in light of its low resource nature? 2)~What is the most promising model? 3) What is the impact of different Large Language Models (LLMs) and prompting strategies on skill extraction (i.e., dynamic vs. static few-shot samples, varying context information, and encouraging causal reasoning)? The article introduces the first Turkish skill extraction dataset and performance evaluations of automated skill extraction using LLMs. The manually annotated dataset contains 4,819 labeled skill spans from 327 job postings across different occupation areas. The use of LLM outperforms supervised sequence labeling when used in an end-to-end pipeline, aligning extracted spans with standardized skills in the ESCO taxonomy more effectively. The best-performing configuration, utilizing Claude Sonnet 3.7 with dynamic few-shot prompting for skill identification, embedding-based retrieval, and LLM-based reranking for skill linking, achieves an end-to-end performance of 0.56, positioning Turkish alongside similar studies in other languages, which are few in the literature. Our findings suggest that LLMs can improve skill extraction performance in low-resource settings, and we hope that our work will accelerate similar research on skill extraction for underrepresented languages.