I went online to make sure my earthquake response is current, it seems to be, and I found this guide published by the LA fire department. It's got a lot of really good information and a number of very useful checklists.
The guide goes more in depth with what to do based on where you are. For general purposes, though, just knowing how and where to duck and cover will help you out. You have two options, get under something sturdy and duck and cover or brace yourself in a doorway. It really depends on where you are at the time. If you're in bed for instance, you want to assume the duck and cover position in bed with blankets and pillows over you. The idea being that if your bed starts sliding around you slide with it instead of being clobbered by other furniture which is also moving around. That's the reason you hold on to a table leg if you're under a table; the table will take you with it.
How to duck and cover
Alright, I know that sounds cheesey, but I grew up doing it and people here in OK didn't. It occurred to me to wonder if people actually know what to do when they're told to duck and cover.
To get into position the first time if you've never done it before goes like this. Kneel on the ground and bend forward so that your head goes toward the ground like you're trying to touch your forehead to the floor. Then put your hands on the back of your neck with your arms next to your head. If you're under something sturdy, wrap one arm around it and bring your hand back to cover your head and neck as best you can.
That's all there is to it, but teaching yourself to do it automatically when the ground shakes takes some time. If you don't have a sturdy table to get under, a door jamb is probably your best bet. For those I usually brace my back against one side while I duck and cover and brace myself by holding on to the molding on the opposite side. If the doorway is too big for that, I cling to the molding on one side.
This is something I feel very strongly about. When I moved to Oklahoma it amazed me that you didn't have to bring your ziploc of emergency stuff to school to be stored with the rest of your class's things. We did that in Cali. Each class would have a big plastic trash can and every child brought in a gallon ziploc with tissues/toilet paper, underwear, and granola bars. I think our teachers had bottled water in the bottom of the cans too. The first aid kit was always near by and easy to get at; we had to take it with us when we left the room for an earthquake drill. We also had a kit at home that had basic things in it in case there was a quake bad enough for us to need it. To this day it baffles me that people don't have tornado kits or anything. Typically, it's a 'grab and go' philosophy if you aren't outside watching for the thing. I've never understood that either.
Anyway, that spiffy guide I liked you to has a great checklist for an emergency kit. The earthquake preparedness kits they suggest will also double nicely for tornado preparedness or the occasional ice storm that we tend to get. If you make a kit, keep it in your tornado hidey hole that way if you make it through a tornado, it should too. Plus that's an area your family will be familiar with and so will remember that there are supplies there.
This is my kit. It lives in my game room closet, which serves as my tornado shelter.
Everything fits neatly into the tub. It's a Rubbermaid style tub that seals pretty well, that way if there's a water leak or the roof blows off my house and it rains all my stuff stays dry.
This is what lives in the tub. It's a little sparse right now, I switch things out in the winter so that everything stays fresh.
A brief rundown on the contents, flashlight, first aid kit, hot hands, poncho (never underestimate the value of a decent poncho, they are remarkably useful), pop top canned goods (no can opener needed and you can use the cans for cups and things after you eat their contents), dry beans, a blanket, batteries, matches, two plastic containers, a plastic cup, fondue pot, face wipes, and cat food. When I'm not refreshing the kit, I have a change of clothes, some liquid fuel, water bottles, toilet paper, and more canned goods in there too.
What you don't see here are the things that are also in the closet. I have a boom box (hence the batteries, that's what they're for), an oil lamp, more blankets, the cat carriers, and a filtering water pitcher. The flashlight is an LED so I don't have batteries in there for it since LEDs barely use any energy. I probably should put another flashlight with accompanying batteries in there though.
It's not a huge kit, but it would hold me and the cats for several days if something bad happened. Using a tub that size means that there is ample room, for those of you who have larger families you could easily fit a change of clothes for each person in there. The pots and cups are my own addition. They aren't normally on lists but I realized at one point that having soups and food was all well and good, but if the rest of my house gets sucked up how the hell would I cook them?
So there you have it. What to do in an earthquake and how to make an emergency preparedness kit.
I must note, for my own safety, that I am not an earthquake or earthquake safety expert. I grew up around them but have had no formal training. This post is intended to be friendly advice, and I cannot be held responsible for any injury or damages that happen to you and yours should you follow that advice. No suing me if you end up getting hurt while taking the steps I talk about. These things can happen even if you try to be prepared, that's why they're called accidents.