Large language models (LLMs) are being widely researched across various disciplines, with significant recent efforts focusing on adapting LLMs for understanding of how communication networks operate. However, over-reliance on prompting techniques hinders the full exploitation of the generalization ability of these models, and the lack of efficient fine-tuning methods prevents the full realization of lightweight LLMs' potential. This paper addresses these challenges by introducing our Rephrase and Contrast (RaC) framework, an efficient fine-tuning framework. RaC enhances LLMs' comprehension and critical thinking abilities by incorporating question reformulation and contrastive analysis of correct and incorrect answers during the fine-tuning process. Experimental results demonstrate a 63.73% accuracy improvement over the foundational model when tested on a comprehensive networking problem set. Moreover, to efficiently construct the dataset for RaC fine-tuning, we develop a GPT-assisted data mining method for generating high-quality question-answer (QA) pairs; furthermore, we introduce ChoiceBoost, a data augmentation technique that expands dataset size while reducing answer-order bias. Apart from these technical innovations, we contribute to the networking community by open-sourcing valuable research resources, including: 1) the fine-tuned networking model referred to as RaC-Net, 2) the training dataset used for fine-tuning the model, 3) three testing problem sets of different difficulties to serve as benchmarks for future research, and 4) code associated with the above resources.