Come up with a survival plan. It's not enough to get supplies. You also need to coordinate with your family. This Red Cross page goes over everything you should discuss—the most important thing is to choose two locations where you should converge to meet one another.
What to do in an earthquake. Drop, get under cover, and hold on. Every kid in earthquake-prone regions learns this in school, but these lessons tend to evaporate during a disaster. Videos from Japan show people standing, running, and trying to keep file cabinets from falling—all major earthquake no-nos. Also, be warned that the Web is littered with misleading advice by Doug Copp, a "rescue expert" who argues that it's dangerous to duck and cover (he suggests lying down next to a large object, like a bed). As the urban-legend-busting site Snopes point out, Copp's theory has been disputed by a number of experts, including the Red Cross. When an earthquake strikes, don't run or try to escape. Search for cover as close to you as possible; if you're in bed, stay curled up and protect your head with a pillow. If you're driving, pull over when it's safe, and stay away from bridges and overpasses.