Started in 1937, morphs into second world war. Actually skirmishes well before that as Chinese nationalist government under Chang Kai Shek struggled to control warlords. Japan wanted to establish control of mainland (Manchuria), particularly given colonial expansion throughout Asia, and had forces throughout China, even in Shanghai. Other East Asian countries obviously see this as an excuse for its own imperialist ambitions.
Japanese army was small but modern in terms of equipment, training and logistic support, and also acted pretty independently from government, who often approved actions retrospectively, but they were surprised when Chinese decided to retaliate to provocation in Shanghai in 1937 (alleged missing Japanese solider, who had actually just gone to bathroom).
Chinese probably never expected to beat Japanese but felt it important to demonstrate to international community that they were prepared to engage in military action. Indeed, they even went as far as catastrophic defensive measures eg flooding of the Yellow River in 1938, which destroyed thousands of villages, killed perhaps a million people and displaced many more. They lost all urban centres (including Nanjing massacre) relatively quickly, but Japanese were unable to control the vast countryside areas.
As European war erupted, Japan decided to take on the ABCD of colonial powers – the Americans, Brits, Chinese and Dutch. America provided logistical support and military advice but no forces (and the American and Chinese generals detested each other). The decision to bomb Pearl Harbour is still hard to understand, presumably they thought America was likely to get involved at some point, and they thought such a strike would make them think again (attacking ships in port is less effective than attacking them at sea, given that many of the crew will be on shore leave, and the ships are more readily salvageable – most of those sunk were indeed brought back into service before the end of the war). Effect was the exact opposite of course – American public opinion had been essentially against military involvement before Pearl Harbour.
The bombing of Nagasaki/Hiroshima is commonly thought to have brought the war to an end but this is untrue. The fire bombing of Tokyo had killed many more people than the atomic bombs did. What brought the war to an end was a combination of Russian involvement in the land war, and the progressive loss of Japanese shipping to provide logistical support to its forces or indeed supplies to Japan.
[In our time, Radio 4]