To fine-tune an existing OpenAI machine learning model, developers need to create an OpenAI account and obtain an API key. They then install the openai and fs npm packages and prepare custom data in a JSONL file format. The prepared data should include prompt-completion pairs that look like text prompts and ideal generated text. Once the data is ready, developers can use OpenAI's CLI tool to fine-tune one of their base models, such as davinci, which allows them to customize an existing ML model with their own data. Fine-tuning helps achieve better results on a wide number of tasks by reusing knowledge gained from solving one problem and applying it to a new but related problem. The process involves uploading the JSONL file to OpenAI's API, creating a fine-tune, waiting for it to process, and then testing the fine-tuned model with a prompt.