Earthquake preparedness doesn't differ a great deal from being prepared for any other type of event. These can knock out power, contaminate water wells and city water systems, make septic issues a real problem, disrupt communications, and even make it impossible to travel to other locations. Because of this, it's important to have a plan and some emergency supplies on hand to last at least three days. (I figure longer, since I'm in a rural area.)
The advice is to NOT run outside in the event of an earthquake unless your actual house is crumbling around you. We are instructed to find a sturdy doorway to stand in. Find a place to get under, like a sturdy table or flipped over contemporary sofas to protect yourself from things that are falling and could injure you.
After the event, if you smell a gas leak, LEAVE! Don't try to find it. Don't try to turn lights on or off. Don't even start your car or cause any sort of ignition source, such as lighting a cigarette. Just leave and let emergency workers deal with the gas leak.
Stay away from downed power lines. The grid could fail completely, but then again, those power lines may still be fully charged and lethal.
Stay in or near your own home if other dangers there don't exist. Don't make it even more difficult for rescuers to find you. Do the best you can where you are.
Have a plan and emergency supplies where you can easily get to them. Include drinking water, non-perishable food, extra clothing, blankets, and any medicines you take.