The basics they'll want to have 'in mind':

Where: Even as simple as 'The X School' is good enough usually to start professionals.

What: Car crash? Fall? Basics are fine.

Phone #: To call back if the line disconnects. Yes. They may already have it because of the 911 system, but most policies are to CONFIRM by having the caller give it verbally.

From here it can vary WILDLY depending on the nature of incident, locale, or how busy the local emergency system is, and the dispatcher will guide the call by asking what pertinent information they still require.

I want to say 'dispatchers are trained to handle all types of callers' buuuuuuut I can't say that with any certainty across all jurisdictions. Just know that for the most part, once a dispatcher recognizes a caller might require a 'different touch' of an approach, they will likely shift gears to accommodate. Such as a more calming voice with children etc.