One of the things they taught us is that during an emergency, local communication will be chaos. It's much more likely to get a line out of town than to people in the same town/province/state as you.
It also really really sucks when fighting for life and livelihood, we have to deal with all the people trying to get in touch to see if we are okay. Of course we aren't okay. Our town has been flattened and there is nothing you can do about it from where you are, please call back later.
To that end, having a designated contact person outside the area that
a) all the people in the disaster can call to check in to say we are okay or communicate that "bob is waiting at the school, sally is at the farm" kind of thing so we can find each other.
b) all the family outside the disaster can call to check up on what we need.
For the events my family has been in or helped give aid to, the Red Cross is often the first on the scene. It's important to register with them if it's a really big thing as they are often the only communication between family inside and outside the disaster. Their big thing is connecting people together and first aid.
After that, it's been the Salvation Army giving food and blankets, etc.
Then the local and then the bigger government aid. Then the other charities.