Federal Emergency Management Agency
FEMA exists to work with external organizations in order to, in their words, "prepare for, protect against, respond to, recover from" disaster.
For starters, try the organization's listings of declared disasters—conveniently sorted by year or state, permitting you to access period-specific information or disasters which were local to your area. Listing content varies. Some merely state that a declaration was issued (which would be an excellent point from which to begin searching local newspapers), while others contain news bulletins. Declarations date from 1953 to present, and cover all 50 states—in addition to the Federated States of Micronesia, U.S. Virgin Islands, Puerto Rico, the Northern Mariana Islands, Guam, American Samoa, the Marshall Islands, the District of Columbia, and Palau.
Another possibility is analyzing a past disaster for governmental process and aid, using the offered disaster declaration definitions and relief procedure. Unclear exactly what hazardous materials, heat warnings, terrorism, or tsunamis entail? Take a look at the various disaster types.
Maybe you would like a visual? FEMA also provides maps, including inundation maps from Hurricanes Ivan, Katrina, and Rita.
Finally, FEMA offers a kids' page. From there, you can access a disaster readiness page, complete with games and appealing animal "guides," which may make historical disasters seem more relevant to those of today. Consider comparing today's disaster kit contents (under "Step 1: Create a Kit") to what individuals would have had in the past. Other options include a multiple choice quiz, information on disaster types, an interactive map of current disasters, and a virtual library. This last contains photos, video files, maps, web links, and suggested reading.