My community does this very well. We do everything through our church groups. Most of the information is spread by people talking to their neighbors, but there are flyers posted in all the city buildings about how to participate and what it is about.
Our philosophy, and that of the city, is that the city will never have the ability to see to everyone's needs in a disaster. So we take care of ourselves and our neighbors and report the big things to the city, like gas lines and water mains.
Most everyone in our neighborhood goes to the same church, so communication on a weekly basis is pretty easy. We are organized by city blocks. Everything is on a voluntary basis. We have volunteer block captains whose job it is to know everyone on their blocks and their needs, i.e. disabilities, widows, oxygen, and to know their resources, like chainsaws, trailers, ATV's, excavation equipment, etc. If you want to keep your preps to yourself that is fine, but our philosophy is that we are much stronger and capable as a community than we ever could be alone. The block captains are by no means 'survivalists', they are just good, caring, responsible citizens. In an emergency, they assess the status of their blocks and report to the neighborhood leader, who reports to the city. We are very lucky to have the support of our church and the city in our efforts.
We don't just prepare for emergencies though. There are several elderly families in the neighborhood who live on an acre or so and have large gardens and orchards. They don't have the means or physical ability to keep up their land, so they enlist the help of the scouts and anyone else who wants to help. The rule is, if you help take care of the garden/orchard, you are free to take whatever you need for your family. Most people just take a few bags of vegetables each week for dinner, there is no hoarding of produce.
All this has taken a long time to achieve and a lot of thought and effort. It also takes support from the city and our church. It also takes good communication between neighbors and a willingness to share and help others. The result is a sense of community, security, and a feeling that we, as a collection of city blocks, can deal with any event that may happen to us.