Ask HN: How does function calling work under the hood?

I would like to understand how a model is returning the right tool to call for a query, what's happening behind the api call for function calling for open ai, mistral and other models.

Are they using a prompt with instructions on how select the right function to call? and when tools and query is passed via api, is the llm using that prompt to select the tool or what's happening behind the call.

How do I achieve function calling using a open source model that I run locally using ollama. Thanks.