How did the war between japan and russia result in the cold war. How was the US and china involved exactly?

The war was actually between Japan and USSR, not Russia. It was fought on land belonged to China with US and Western allies watching and supporting the Chinese govt.

Japan was the aggressor and invaded part of China bordering USSR. To protect its own interests in China, USSR fought off Japan and took over the puppet govt in Manchuria set up by Japan. It allowed USSR to spread communism to China which turned into a communist country later. US and Western allies won WWII but were alarmed to see the spreading of communism. That confrontation was the beginning of the cold war.

The Soviet-Japanese War was part of the Second World War fought in China. Japan had set up a puppet state of Munchukuo in northern China; threatening Soviet's interests in the area. The Soviet invaded and took over control of Manchukuo.

Japan surrendered but the Soviet stayed in northern China and supported the communist movement in that country. China eventually became a communist country and fell under Soviet's influence.

US and western allies were very concerned about the development. The Chinese government they supported failed to the communist army. They ended up starting up NATO as a counter to the Warsaw Pact led by the Soviets. That resulted in the Cold War.