There is not so much need to worry about what will happen in a disaster if you plan for what you will do and prepare for it. It is not a really difficult thing to do if you find out what you will need and break down what you need to have and do to get ready.
There are several government agencies and nonprofits that have information available to the public about what to do in a disaster. I will provide links to some of them in this blog post.
There are two main ways to deal with a disaster. One is to evacuate to a safer place, perhaps a shelter that has been set up for people who have been evacuated. The other is to stay put and "shelter in place". If local authorities tell you that it is necessary to evacuate, you need to pay attention to them and evacuate. People who do not do this often end up dead. If you are told that it is ok to stay put and take shelter in your home, then you can shelter in place.
I believe the most important thing for you to have when a disaster happens is information. You need to know that the disaster has happened, what kind of disaster it is and whether the local authorities want you to evacuate. If you need to evacuate, you need to know where your shelter will be and safe ways to get to it. The emergency alert system tests that stop your radio and TV programs are to make sure the system works right in a disaster. The regular stations will stop normal broadcasting during an emergency alert and tell you where to tune in to find out what you need to know about the emergency.
There are many kinds of disasters and it can be overwhelming if you think you have to prepare for all of them at once. Relax, you do not need to do everything at once. There are certain things you will need in almost any disaster that are the same. Once you look at lists of disaster preparedness items you will see that once you are ready for one kind of disaster, you will be mostly ready for most other types of disasters.
The lists on the sites I am giving you links to are very comprehensive. They are meant to cover what many different people and families might need. Every person and every family is different. You and your family will probably not need everything on the list. You can start with what you think is most important. and work your way down to the less important and things you may not need at all.
If your time and budget are limited, you can prepare just a little bit at a time. You can start with being prepared for a disaster that lasts only a few hours and work your way toward longer term ones. One meal at a time for you and your family to be able to eat during a disaster is ok as a starting place. Next you can prepare for a whole day and then three days, and so on.
I would like to suggest that you prepare a "go bag" first. This is a package that you can easily carry, backpacks are good, in case you are in a disaster where you have to evacuate. The sites I will give you links to will have lists of suggested items for go bags. There may be items not listed that you will want in your go bag and the go bags for your family. Again, go bags are as different as the people who make them. You will probably not need everything on the go bag list.
Here are some sites with information about preparing for disasters and lists of suggested items for preparedness for go bags and sheltering in place:
This link to FEMA explains about Go Bags
This is FEMAs list of basic supplies.
PDF short basic list of supplies
This link has FEMAs ideas for making your disaster plan.
FEMAs ideas for plans depending on where you are when a disaster happens.
FEMAs in depth guide to preparedness
The list of preparedness supplies starts on page 31 in the last link. You will probably not want to start right off with FEMAs in depth guide to preparedness, because it is very long and has a lot of information to digest, but you can copy it and maybe print it out so you can get ready to read it later. Don't postpone this indefinitely, though. Most of us like to procrastinate and that can be fatal. This needs to be a priority for everyone. You could die if you are not ready to evacuate and have to run around grabbing things and looking for them at the last minute. Avoid that by being prepared.
I am going to do another post, or several, on other disaster preparedness sites because this one is getting too long. I want to make this easy to read for people who are not used to preparedness.