Short answers, pulled from the story.
The Battle of Moscow was a series of two engagements fought on the 1st and the 3rd of September 1612, during the Polish-Russian War of 1609-1618 and the Time of Troubles. Both battles ended in decisive Russian victories, forcing the Polish-Lithuanian relief army under Field Hetman Jan Karol Chodkiewicz to withdraw.
Prince Dmitry Pozharsky commanded the Russian forces at the Battle of Moscow in 1612. He led the Second People's Militia, which had been organized by Kuzma Minin, a citizen of Nizhny Novgorod. Don Cossack forces under Dmitry Troubetskoy also played a decisive role in the first engagement.
Field Hetman Jan Karol Chodkiewicz commanded the Polish-Lithuanian Commonwealth forces at the Battle of Moscow in 1612. He led the relief army attempting to break the Russian siege of the Kremlin garrison, which was commanded by Mikołaj Strus.
After the Battle of Klushino in the summer of 1610, Tsar Vasili IV was deposed and taken to Warsaw. The Polish-Lithuanian army then occupied Moscow on the 21st of September 1610, and the city's boyars, clergy, and citizens accepted the Polish prince Wladyslaw IV Vasa as their new tsar out of fear of the pretender False Dmitry II.
After the Polish garrison surrendered unconditionally on the 27th of October 1612, it became necessary to choose a new sovereign. In 1613, the Zemsky Sobor held a meeting in the Kremlin and elected Mikhail Romanov as tsar of all Russia, establishing the House of Romanov and marking the end of the Time of Troubles.
The Second People's Militia, assembled by Kuzma Minin under the command of Prince Dmitry Pozharsky, was better armed and organized than the First People's Militia led by Prokopy Lyapunov. The First Militia failed to take the Kremlin and fell into disorder after Lyapunov was murdered by the Cossack leader Ivan Zarutski in 1611. The Second Militia took Yaroslavl in March 1612, established a provisional government, and drew support from cities across Russia including Siberia.