Short answers, pulled from the story.
The Time of Troubles began in 1598 with the death of Tsar Feodor I, the last ruler of the House of Rurik, and ended in 1613 with the election of Michael I of the House of Romanov by the Zemsky Sobor. The fifteen-year period encompassed famine, civil war, and foreign occupation.
The False Dmitrys were impostors who claimed to be Tsarevich Dmitrii, the youngest son of Ivan the Terrible. False Dmitry I appeared in the Polish-Lithuanian Commonwealth in 1603 and was crowned tsar in Moscow on the 21st of July 1605; False Dmitry II emerged in July 1607 and set up court in Tushino, besieging Moscow for eighteen months; False Dmitry III appeared in Novgorod and then Pskov in 1611.
Estimates of total deaths range from one to 1.2 million. Some areas of Russia experienced population declines of over fifty percent, and the cultivated area of central Russia shrank by several times its previous extent.
The famine of 1601-1603 was potentially caused by the eruption of the Peruvian volcano Huaynaputina, which produced nighttime summer temperatures that repeatedly dropped below freezing and destroyed harvests. Contemporary accounts suggest it killed between a third and two thirds of the Russian population.
Kuzma Minin was a butcher from Nizhny Novgorod who organized and funded the second national militia in the fall of 1611 by collecting taxes from the local population, monasteries, and crown peasant villages. He recruited Prince Dmitry Pozharsky to command the force, which liberated Moscow from Polish occupation when the Kremlin garrison surrendered unconditionally on the 27th of October 1612.
The Zemsky Sobor elected Mikhail Romanov, the sixteen-year-old son of Patriarch Filaret of Moscow, as tsar on the 21st of February 1613, ending the succession crisis. He was crowned on the 21st of July 1613, founding the Romanov dynasty that ruled Russia until the February Revolution in 1917.