This is a good opportunity so I'm gonna post what I, a native-born Japanese, have been always thinking: This country is literally shaped by earthquakes. This is true not only in a geological sense but it also applies to the culture. Earthquakes affect how all the buildings here are made, the way of transportation, and virtually every aspect of our daily life. We always fear them and talk about them, but we're kinda resigned to accept the fate. This concept of resignation is seen in many ways in the Japanese culture. But it's also earthquakes that make us truly united. I realized this when the big quake hit the country five years ago. As much as we hate them, we are defined by earthquakes.
Similar to the Netherlands, where almost 2/3 of the country's inhabitants live below sea level. We are defined by our relationship to the sea, and you can see how that's related in how we build our cities and farm our land. It's also seen in our tolerance to views/perspectives different to our own - how petty do our differences seem when the sea is indifferent to our squabbles?
Something that's missing there: don't use elevators during or immediately after a quake.
IMO the single most important thing is: when you're at the beach or close to the coast at sea level make sure you know where the nearest evacuation area is.
It is very unlikely that you'll see an earthquake that is strong enough to be dangerous. Japanese buildings are very resilient. Even this rather strong quake has caused only minimal damage.
First of all don't worry. Even if you see large death and injury tolls, the percentage of people injured or killed is surprisingly small. Economically and socially, it is a huge burden, but the vast majority of people in Japan experience large earth quakes with no physical injury.
A couple of key points (anyone who knows better, please correct me!): if an earthquake strikes, don't panic. Just stay where you are. Trying to walk -- especially trying to go down stairs while the earthquake is happening -- can cause serious injury. Wait until everything stops shaking (usually a few seconds, but can potentially last up to a minute for a huge earthquake.). If you are near large, unsecured furniture, it might be better to edge yourself away. Many people get killed by bookshelves falling on them. All hotels I've been to in Japan have had furniture affixed to the walls, so you are pretty safe in a hotel.
Next if you are inside a house, after the shaking (in this order) turn off the gas shut off and open the doors. If you are in a safe place, don't leave. Fill your bathtub with water, in case the water shuts off. Check the news on TV or radio for further instructions. There will also be an announcement over the public speaker system, but it will be in Japanese only. If you are in a hotel, ask for assistance.
In the case that there is a tsunami warning, evacuate to high ground. These days there are signs in every neighbourhood denoting the height above sea level. While you are walking around, keep note of them. In low lying areas, there will be tsunami evacuation centres. Keep an eye out for them -- they can be normal apartment buildings. There is a sign on the door (usually in English too).
If you are outdoors when an earthquake strikes, again, wait until it has stopped shaking. HOWEVER: note your surroundings. If you are next to a brick building or large glass windows, etc, pay extra attention for falling debris. After the shaking has stopped, try to find a space away from buildings and telephone poles (hard to do in the city, but...) Wait for further instructions.
By and large, you can simply follow what other people are doing and it will most probably be fine. We have earthquake drills in my home town something like every month and people know what to do.
In any case, you are tremendously unlikely to encounter a really large earthquake while you visit. I've been here for about 8 years now and I've only experienced 1 really big one. We get several small ones from time to time, so you have a decent chance of experiencing those -- they are surprising, but you don't have to worry about them. Generally speaking, if you are still able to stand and walk while an earthquake is happening, then there is virtually no chance of injury in Japan. If you get thrown to the ground or literally couldn't take a step if you tried, then it's very, very serious.
That really isn't that out of the ordinary. Areas that are particularly susceptible to wildfires tend to have a constant pervading theme of understanding your home can be turned to cinders. Coastal areas have flooding and, depending on the region, hurricanes. And so forth.
It is a fundamental part of the human condition. People who live in places where people probably shouldn't either leave or get used to it.
A big tsunami like that happens about once every 500 years. It the life of the nuclear plant is 50 years, the risk of a disaster happening was 1/10. I don't think that this was an acceptable risk. Even a risk of 1/100 or 1/1000 would be unacceptable.
That means that the nuclear plant should have never been there, or should have been prepared to be run over by a tsunami...
Or the walls 1m taller, or build it underground, or not build it at all. But it does not make sense to build a nuclear plant saying "yes, well, maybe it will be ok"!
Wasn't the problem that the power mains coming in to the station got cut? Apparently the power station needs external power feeds to maintain the control machinery?