Short answers, pulled from the story.
The Soviet Union and Nazi Germany signed a ten-year non-aggression pact on the 24th of August 1939. This agreement contained a secret protocol that divided Northern and Eastern Europe into German and Soviet spheres of influence.
Seventeen days after the German invasion of Poland, the Soviet Union entered the eastern regions of Poland. They annexed territories totaling 201,516 square kilometers with a population of 13,299,000.
On the 5th of March 1940, members of the Soviet Politburo signed an order to execute POWs labeled nationalists and counterrevolutionaries. This event became known as the Katyn massacre where some 22,000 were executed.
On the 16th of August 1945 the Communist-dominated Provisional Government of National Unity signed a treaty with the USSR to formally cede these territories. The total population of the territories annexed by the USSR had an estimated population of 10,653,000 according to the 1931 Polish census.
From 1944 until 1952 the Ukrainian Insurgent Army were engaged in an armed struggle against the communists. As a result of skirmishes between the UIA and Soviet units, the Soviets deported 600,000 people from these territories.