Short answers, pulled from the story.
The invasion began with a border assault on the 11th of August 1945, followed by landings at Tōro on the 16th and at Moeka on the 20th. Fighting continued until disarmament was completed on the 23rd of August.
The invasion was led by the 2nd Far Eastern Front under General of the Army Maksim Purkayev, through its 16th Army commanded by General Leonty Cheremisov. Admiral Ivan Yumashev's Pacific Fleet provided naval support.
Fifth Area Army Commander Lieutenant General Kiichiro Higuchi ordered the 88th Division to defend South Sakhalin at all costs, fearing a Soviet advance toward Hokkaido. This came even after the Imperial General Headquarters had ordered a ceasefire under Order 1382.
Japanese military deaths are estimated at 700-2,000, alongside roughly 3,500-3,700 civilian deaths. Soviet records list 18,302 Japanese soldiers taken as prisoners of war.
Tōro's mayor, Shōmatsu Abe, was taken hostage and executed while trying to negotiate a ceasefire. At Moeka, civilians mistaken for soldiers were executed on the beach, and employees of the post and telegraph office took their own lives together.
South Sakhalin has remained under Russian control since the Soviet occupation was completed on the 25th of August 1945. It is now part of Russia's Sakhalin Oblast, though Japan continues to dispute the territory's status.