How was korea split between the United States and the Soviet Union?
The demarcation of Korea into North and South was largely an accident in the final days of the Second World War as the Allies rushed to work out the occupation of Japanese-held territories.
As 1945 drew onwards, the United States and the Western Allies had been more concerned about convincing Japan to make an unconditional surrender than about how the occupation would undertaken. It is also clear in retrospect that the US had given very little thought to Korea at all and knew little about it.
The USSR had to be reminded of their treaty obligations with the rest of the United Nations (the name then applied to those countries which had been engaging the Axis powers). The Potsdam Summit in Berlin in July 1945 saw the Soviets commit to attacking Japan, however, Stalin had a very clear idea of regaining territory Russia had lost to Japan in 1905, and in strengthening its position vis-a-vis China.
The US, already starting to get a clear idea of Soviet occupation behaviours in central Europe, also decided it didn't want to let the Soviets onto Japan.
The Soviets declared war on Japan on August 8th, and on the 15th, the Japanese announced a cease-fire. Japan's surrender was signed on September 2nd. The decision to split Korea along the 38th Parallel was a hasty one made after Japan announced the ceasefire; North Korea could be easily entered by the Soviets, but South Korea would put the Russians too close to Japan. Using a line of latitude to demark seperate occupation zones clearly indicated a lack of knowledge of Korean conditions.
The Americans arrived in South Korea on September 8th, to disarm the Japanese, and stabilize South Korea until Korea organized itself. The Soviets in the north were doing the same thing, but --as they did in Europe -- created a Marxist-Lenist regime, while the Americans tried to create a democratic state in the south.