Short answers, pulled from the story.
The Treaty of Brest-Litovsk was signed at 17:50 on the 3rd of March 1918. It was signed at the fortress city of Brest-Litovsk, now Brest, Belarus, between Soviet Russia and the Central Powers: Germany, Austria-Hungary, the Ottoman Empire, and Bulgaria.
Russia lost 34% of its population, 54% of its industrial land, 89% of its coalfields, and 26% of its railways. The ceded territories included Ukraine, Poland, Belarus, Lithuania, Latvia, Estonia, and the Caucasian districts of Ardahan, Kars, and Batumi.
Grigori Sokolnikov signed the treaty on behalf of Soviet Russia. He arrived stating that Russia would sign immediately without entering into any discussion of the terms, treating the document as an ultimatum.
Lenin argued that signing a harsh peace was preferable to further military humiliation after 53 Central Powers divisions advanced against near-empty Soviet trenches. He told the Central Committee they must sign "this shameful peace in order to save the world revolution," warning he would resign if they refused.
The treaty lasted less than nine months. It was abrogated by one of the clauses of the Armistice of the 11th of November 1918, and the Bolshevik legislature formally annulled it on the 13th of November 1918, with the annulment published in the newspaper Pravda the following day.
Trotsky replaced Adolph Joffe as the Soviet delegation's leader with an explicit strategy of prolonging the negotiations to await revolutions in Central Europe. He proposed the "no war, no peace" formula and later resigned as foreign minister after the treaty was signed, being replaced by Georgy Chicherin.