The fighting of the Korean War was mainly between the troops from North and South Korea, the UN and China. Hence, some might think that Russia had little effect on the progress of the war. However, Russia did have a say in the war: in fact, it turns out that the war would not have started without Russian support on the side of the North Koreans.

After World War II, Russia believed that a reunification of Korea could still take place. Hence, Stalin was not planning to initiate an attack of South Korea from North Korea. Instead, he was actually afraid that South Korea would attack first, so he avoided offending the US and South Korea. This attitude continued through early 1949, when Stalin was informed of the increasing number of violations of the 38th parallel, where North and South Korea are divided.

It had been believed that Stalin commanded Kim to start the Korean War. Instead, Russian documents declassified in the early 1990s reveal that it was Kim who asked Stalin for permission to go to war for nearly a year before Stalin finally approved of it. Indeed, during Kim's visit to Moscow in March 1949, he told Stalin that the reunification of Korea was only possible "through military means". Stalin refuted this point, stating that North Korea did not have as large an army as South Korea. Also, Stalin said that North Korea should only attack South Korea after the South launches an attack first.

However, North Korea did not stop putting pressure on Russia to start an invasion of South Korea. This continued persuasion worked; Stalin finally gave in to Kim's requests in January 1950, and promised to help plan the invasion as long as risks of failure of reunification are minimised. To this end, Stalin provided the North Koreans with munitions and advisers, who drew up the entire battle plan for North Korea. The actual invasion was carried out on 25 June 1950, under the excuse that the South Korean border guards shot at the North Korean guards (this incident was also caused by the North Koreans themselves).

It is not clear what prompted Stalin to make this decision of offering assistance to North Korea, but possible factors include the successful establishment of Mao's communist government in China in 1949, which might lead him to believe that a similar revolution is feasible in other areas. Also, there was the desire to eliminate the only ally of the US in mainland Asia, so as to consolidate the position of the USSR as a world superpower, with a large part of Asia under its influence.

However, Stalin would not have joined the Korean War if not for the continuous persuasion by the North Koreans that there was no other way to reunite Korea than by force. All preparation by Russia for North Korea for the Korean War was under the pretext that North Korea actually succeed in their operation, and that this war would be swift enough to not allow any time for the US to intervene. Stalin placed this as the top priority, as he absolutely did not wish for a third World War to happen. This explains why he ordered all advisers and ships off the front line, and did not openly support North Korea for a full week, after the UN troops landed in Incheon on 15 September 1950. Thereafter, all Soviet involvement in the Korean War had been kept confidential.

Interestingly, the Korean War was useful to Russia in a way unforeseen before the war. When Russia could participate in the war under cover, Stalin realised that he could use this as an opportunity to find out about US technologies, in particular the F-86 Sabre which rivalled the Soviet MiG-15. This was the main reason why the Korean War dragged on for so long in stalemate: Stalin could veto armistice agreements proposed by the Security Council indefinitely, to continue gathering intelligence through the war. This period finally ended with the death of Stalin in March 1953, and the ceasefire took effect relatively quickly on 27 July of the same year.

Sources:
Lashmar, Paul, "Stalin's 'hot' war": http://www.mtholyoke.edu/acad/intrel/lashmar.htm
The Origins of the Korean War: http://www.alternativeinsight.com/Korean_War.html