In the USA, if you dial 911 from a landline phone, the Public Safety Answering Point (PSAP) will immediately have your address. For multi-tenant residential buildings they'll get the unit number. With few exceptions, in large commercial buildings they'll get a location (like "3rd floor, SE quadrant") or even a room number.

If your phone has GPS capabilities, they're turned on, and the phone has a good-enough view of the sky to get a fix, the PSAP will get the GPS location of your phone. If you haven't been using any features that use GPS, it's possible that later in the call the PSAP will get a better fix. Phones that use aGPS (like the iPhone) will provide the more precise location fix that aGPS provides if it's available. My understanding is that on the iPhone, if Location Services is turned completely off that navigation is off and this feature will not work for 911 calls. If Location Services is turned on at all (even if it's turned off for all apps that can use it) the location is provided to the network for 911 calls.

Without regard to whether Location Services is turned on the PSAP will obtain cell tower location data. If you're in range of only a single tower, they'll get the tower's location. If you're in range of three or more towers, they'll get an approximate phone location based on triangulation.

Two of my daughters are old enough to carry cellphones. I have trained them that when calling 911 the first words out of their mouths should be the location they are calling from.