There is no fine-tuning. They simply use prompt engineering. See Section 3 for "Method", they have a short, easy-to grok motivating example, I don't think you need to be an expert in planning to see what they do.
To summarise, they assume a human expert can provide a domain description, specifying all actions that can be taken at each situation, and their effects. Then it looks like they include that domain description to the prompt, along with an example of the kind of planning task they want it to solve, and get the LLM to generate PDDL in the context of the prompt.
To summarise, they assume a human expert can provide a domain description, specifying all actions that can be taken at each situation, and their effects. Then it looks like they include that domain description to the prompt, along with an example of the kind of planning task they want it to solve, and get the LLM to generate PDDL in the context of the prompt.