End of WWII
After the end of WWII, the Soviet forces and American forces were working together to defeat Japan. They both attacked Korea, and so the Japanese surrendered to the Soviet forces north of the 38th parallel, and the American forces south of the 38th parallel.
North Korea launches surprise attack
North Korea launched a surprise offensive. This started the war. President Truman was worried that North Korea was acting like Hitler had, and wanted to stop this. When South Korea complained to the United Nations, the USSR was not there in protest, so could not stop the UN from sending soldiers to aid South Korea.
The Allied forces push the border north
The UN soldiers were sent in to push the border northwards. This effort was lead by Douglas McAurthur. In fact, they pushed so far northwards that China got worried.
China joins the war to push border back south
When China joins the war, they overwhelm the UN forces, and push the border back south again. This supports the Domino Theory.
In 1953, American and North Korean forces signed a cease-fire agreement. This ended the war, and has remained the way until the present. There is a demilitarized zone in between the two countries.