I can tell ya exactly:
"9-1-1, where is your emergency?"
(ideally) "123 Main street."
"123 Main street? What's going on there?"
"This girl is trying to kill me!"
"Is she there right now?"
"Yes, I've barricaded myself in my room."
"Okay, try to stay calm while we get police on the way. They're coming as fast as they can. Do you know who is trying to kill you?"
"Suzy McKillerson."
"Can you describe her?"
"She's 5'5, 105 lbs, long brown hair."
"What is she wearing?"
"A bloody apron and blue jeans."
"Is she armed?"
"She's got a knife!"
"Okay, police are on the way to 123 Main Street. Is she in the house right now?"
"Yes, she's trying to break down the door."
From there, it's a matter of keeping the police updated as to the suspect's whereabouts. If I feel like you're safe enough, I'm going to figure out why she's trying to kill you, the nature of your relationship, if she has a vehicle and what kind it is, and so on. In almost no circumstance will I let the caller try to disconnect with me. You can't prevent people from being stupid however, and they will often hang up and call a relative for no good reason.
If the suspect is NOT on the scene, then the call will proceed much the same, with a stronger focus on suspect description, possible date of birth (so we can pull her driver's license,) known history of violence or stalking, if she's known to carry weapons, and so on. Even when we're skeptical
"She's going to release a panther in my house trained in ninjitsu!"
we'll still send an officer. Just because a person is crazy doesn't necessarily mean they are not in danger.
