Document Information Extraction (DIE) aims to extract structured information from Visually Rich Documents (VRDs). Previous full-training approaches have demonstrated strong performance but may struggle with generalization to unseen data. In contrast, training-free methods leverage powerful pre-trained models like Large Language Models (LLMs) to address various downstream tasks with only a few examples. Nonetheless, training-free methods for DIE encounter two primary challenges: (1) understanding the complex relationship between layout and textual elements in VRDs, and (2) providing accurate guidance to pre-trained models. To address these challenges, we propose Sample-centric In-context Learning (SAIL) for DIE. SAIL introduces a fine-grained entity-level textual similarity to facilitate in-depth text analysis by LLMs and incorporates layout similarity to enhance the analysis of layouts in VRDs. Additionally, SAIL formulates a unified In-Context Learning (ICL) prompt template for various sample-centric examples, enabling tailored prompts that deliver precise guidance to pre-trained models for each sample. Extensive experiments on FUNSD, CORD, and SROIE benchmarks with various base models (e.g., LLMs) indicate that our method outperforms training-free baselines, even closer to the full-training methods. The results show the superiority and generalization of our method.