The authorities advocate for two types of emergency preparedness: The first is caused by the increased fire risk when houses are built of wood. Know how to get out of any room in your dwelling and make sure that your children also know. Have a safe spot where you have arranged to meet. A good spot is out of the range of fire and not under an electric pole or close to something else that is likely to tip over in an earthquake. Because earthquakes are the other main hazard that you should be prepared for, and you may want to use the same meeting spot.
Obviously you don't want to run around while the earth is actually quaking. During the earthquake, the routine taught in the schools is "duck and cover" - dive under the nearest table (that doesn't have a glass tabletop), and hang on to the legs of the table while keeping your head down. If the roof caves in the table will protect you, but you don't want the table to jump around during the shaking, it may step on you or move away from you so you are no longer covered. If no table is around, stabilize yourself in a doorway or drop down next to a sofa or other sturdy piece of furniture that may protect you from a falling ceiling.
Next, after saving yourself, you want to make sure that your possessions are not adding risks to your safety. Big bookcases and heavy dressers can become surprisingly unstable when shaken. If all drawers of a dresser are open at the same time it will topple over. The local hardware store has a section with anchors and straps for securing your furniture.
Likewise, your kitchen cabinets will open and send the contents all over - unless you secure it somehow. Kids safety locks work well but may be a hassle for cabinets you open all the time. They may however, be the right thing for the display cabinet with your inherited porcelain. For cabinets often in use a rubber band can perhaps minimize the damage?
As a general rule you don't place beds underneath windows. Earthquake safe glass is code for new buildings, It is laminated like car windows and will not splinter. But if you rent or buy an old house, you can still find windows that are a nightmare to clean up if they break and a safety hazard in earthquakes.
As houses are heated with gas, you want to have a wrench strapped next to your gas-main so you easily can turn off the gas in case a quake has broken your pipes. For the same reason your water heater must be strapped and a foot off the ground. You don't want it to fall over and drown out the flame without the gas being turned off.
So let us say that there has been a big quake and you are safe but the infrastructure is not; gas, electricity, and water pipes don't work. What will you need? Light, water, and provisions for 3 days+. Light means flashlights and extra batteries. Water - at least a gallon a day per person. That is 12 gallons for a family of 4. Food that will not spoil and can be prepared without the use of your stove or oven. Typically this means energy bars, cereals, rice, pasta, cans of misc. food. stored somewhere accessible if the house is in ruins.
We have additional propane tanks for our backyard gas grill. Even without electricity your frozen items will not spoil for a day or two but the content of the refrigerator will only last a day. So if you can get to your fridge and freezer use that first and wait with the dry food until later unless you have to evacuate.
A case of UHT milk will be popular with the kids. Then they can have cereal and milk, or just a glass of milk - even if it is not as cold as could be hoped for. You can rotate the milk containers through the lunch boxes so you always have a reasonably fresh case. It usually spoils after 3-4 months. Tea and ground coffee will be popular with adults and if you have a box or two of cookies in reserve nobody will but thank you.
A first aid kit, sleeping bags and a tent are not bad additions to your supply. Even if you are not usually a camping person, you - or your neighbors if their house is in even worse condition than yours - may be thankful for alternative shelter if your house is filled with broken glass and a caved in ceiling.
Finally you may want to have a radio running on batteries for getting updates about help from outside forces (and extra batteries), a solar charger for you phone, a wad of cash somewhere safe for when the credit card machines don't work, and you will be thankful that you have gotten into a routine of always filling up your car when it is half full, not waiting until it runs dry.
If you live off the beaten path with some distance to the nearest fire station, or in mudslide or flooding territory, your emergency supplies should be stored for easy evacuation. In an earthquake you can usually get back into the ruins once the ground has stopped shaking, but if you need to evacuate and can't get back into your house you will also need changes of clothes, toiletries, towels...
Hopefully you will not experience an earthquake but otherwise think back to the conditions after Hurricane Katrina and ask yourself how you would have survived if the help from outside forces was as unreliable as what was displayed then.
Chance is, however, that you may experience a black out. Gas and water works, but no electricity. Consider that a rehearsal for "the big one" - and pack that emergency kit!