Building high-quality datasets for specialized tasks is a time-consuming and resource-intensive process that often requires specialized domain knowledge. We propose Corpus Retrieval and Augmentation for Fine-Tuning (CRAFT), a method for generating synthetic datasets, given a small number of user-written few-shots that demonstrate the task to be performed. Given these examples, CRAFT uses large-scale public web-crawled corpora and similarity-based document retrieval to find other relevant human-written documents. Lastly, instruction-tuned large language models (LLMs) augment the retrieved documents into custom-formatted task samples, which then can be used for fine-tuning. We demonstrate that CRAFT can efficiently generate large-scale task-specific training datasets for four diverse tasks: biology, medicine, and commonsense question-answering (QA), as well as summarization. Our experiments show that CRAFT-based models outperform or match general LLMs on QA tasks, while exceeding models trained on human-curated summarization data by 46 preference points. CRAFT outperforms other synthetic dataset generation methods such as Self- and Evol-Instruct, and remains robust even when the quality of the initial few-shots varies.