So strange... I live in Shanghai, but I haven't seen anything crazy like this happen.. well, early days yet.
Let me summarise this, as to how I understand the history over here:
1) 14th century, China claims islands
2) 1890 Japan takes over islands (in a war)
3) WWII America takes over islands
4) 1970 America gives islands back to Japan, China doesn't object or say anything
A few days ago we had an air-raid drill across China, you know, those sirens you hear in Silent Hill (also from WWII) as the world changes before you... I didn't know it was a drill and promptly began sh*tting myself.
Aside from the resources that can be gained from owning these islands (gas deposits and oil, I believe), the biggest motivation for this conflict is "face"... a concept many in the West have difficulty understanding.
This concept of "face" as well as thousands upon thousands of years of culture and history is easily scoffed at by people of the West; for it is considered beneath them. China refuses to be seen as weak, in the past it has been exploited by the West and Japan many times...
Japan refuses to acknowledge what is had done during WWII. They even refuse to educate their younger generations as to what they did to China during the invasion. Japan also has shrines for the fallen soldiers and "heroes" who massacred and raped China and they are often commemorated, worshipped, etc.
Imagine if Germany had shrines to the "heroes" who helped exterminate the millions of Jews in the extermination camps and to the "heroes" who blitzed London... maybe now you have a small insight as to how delicate things are over here.
It is difficult to understand things foreign and easy to draw comparisons to the limited experiences we have. Many people in the UK think it is bat-sh*t crazy, that people in America can walk the streets with guns, therefore they assume people are getting shot; left-right and center... it is easy for the people of UK to say "Hey, why don't you Americans just ban guns? We do, in the UK... simple" However, there are those in the UK who can look past these simplified and arguably ignorant remarks and reach understandings as to why America does what it does.
Educate yourselves. Look into the history of these islands. Look at both sides of the stories. Travel to China and Japan. Talk to the people.
[edit: typo]