On September 17, 1939, Soviet forces crossed Poland's eastern frontier in six armies, and by the end of the month they had taken roughly half the country. The invasion began sixteen days after Germany attacked from the west, while the Polish army was still fighting and Warsaw was under bombardment.
It was not improvised. The Molotov-Ribbentrop Pact of August 23, 1939, had a secret protocol dividing eastern Europe into spheres, with Poland split along the Narew, Vistula and San rivers. Stalin had waited, and the reason he waited was that he wanted to see how the German attack went and whether Britain and France would fight. Once Warsaw was clearly going to fall and the Polish government had left for Romania on the night of the 17th, he moved. Molotov announced that the Polish state had ceased to exist and that the Soviet Union had a duty to protect the Ukrainians and Belarusians inside it.
The Poles were fighting two enemies and knew it. The eastern frontier was thinly held because the army was engaged in the west, and Commander-in-Chief Rydz-Smigly ordered his troops not to fight the Soviets and to withdraw into Romania and Hungary instead. Some units did fight anyway. Grodno held for three days. About 250,000 Polish soldiers ended up in Soviet hands, and the officers among them were the ones the NKVD shot at Katyn and elsewhere in the spring of 1940, some 22,000 of them, a massacre the Soviet government denied until 1990.
The two armies met at Brest-Litovsk and held a joint parade on September 22, then adjusted the line: Germany took more Polish territory and Lithuania fell to the Soviet sphere. Poland disappeared from the map for the second time in its modern history, and it would be partitioned a third time before the war ended.
What followed in the annexed territory was deportation on a large scale: four waves between February 1940 and June 1941, perhaps 1.5 million people sent east, to Kazakhstan, Siberia and the Arctic, in cattle wagons, with executions and camps for those the Soviet state regarded as dangerous. The Soviet government called the whole thing reunification. The borders it took in 1939 are close to the ones it kept after 1945.