If an airline has an accident, the chances are you (as the next set of passengers to board that plane) will be the least of their concerns - if there's an incident then it tends to be a case of all hands to action stations to deal with the media, emergency services, families of any potential victims, provide assistance where possible etc. That said, they do have some procedures they attempt to follow. These vary a little from airline to airline.
Most will make an attempt to contact you via text/email if they have it or via the GDS to your travel agent, depending on how far away you are from your departure day/time. It also depends whether you gave contact information to the carrier or your travel agent, whether your travel agent passed it on or, indeed, whether you used a travel agent at all.
The next set of passengers rightly tends to be second priority after dealing with the incident, however. Often if you're on the next flight, therefore, the communication will be a little slow and the first you'll know about it will be when you arrive at the airport - also remember that there's a good chance you're already at the airport, or are on a connecting flight.
If you get to the airport, you'll likely be informed by the staff there who will attempt to get you onto another flight with the same company or another carrier.
As an addition from the comment below, if you're a family member etc who's signed up to flight alerts from the airline in order to hear about delays/diversions etc (some airlines provide this as a service to avoid inconvenience and avoid too much waiting traffic at the terminal), then you'll likely be one of the first priorities. The system is normally set up to send automated or manually-triggered pre-written messages, but in an emergency will usually be used to send a manual message to relevant family members etc.
Obviously this only applies if you've signed up to the service, and only usually applies to the airline's own service: if you've signed up with a third party flight tracking service, they likely have no more information than you do.