Earthquake... How to react?

One day at about 8pm I was playing with my brother. I felt some shake, and my mom shouted “earthquake” and rushed in and carried my brother . We ran outside the house. We noticed that there was no one except us in the apartment who came out. We have recently moved to California from India. Next day I asked my friend about it and he said his teacher has instructed not to go out but have to DROP to the ground; take COVER by getting under a study table or other piece of furniture or get into toilet or bedroom where there is double ceiling. Next day a similar announcement was made in my school too. I searched in the web and found similar information. Refer:
http://www.consrv.ca.gov/index/Earthquakes/Pages/qh_earthquakes_what.aspx
http://www.fema.gov/hazard/earthquake/eq_during.shtm

But, my awareness on this earlier was different. My Mom read out an article for me after the 2005 Tsunami in India which explained to get out of the building to an empty ground or how to stay safe in the triangle formed by the objects falling towards ground from top. The strict instruction was not to get below any table/cot to avoid crushing.

I was confused by the instruction that is totally opposite .

I asked my uncle about it and he said the building in US are earthquake proof. I know that houses are made of wood here and walls between rooms are only false partitions. I do not understand what earthquake proof means. Here apartments have multiple floors. If the ceilings in the top floor are heavy enough to hold people and their furnitures would it not cause damage if it falls?
In India houses are made of bricks , cement and iron bars .
If people who lived in US for quite sometime in US goes to places like India and follows the practice they have here when they face an earthquake, then would it not cause a serious damage to them?
I also didn't know what is double ceiling ? and how does it protect us during an earthquake?