Short answers, pulled from the story.
Moscow was established as a separate principality when Daniel, the youngest son of Aleksandr Nevsky, received the city as an appanage. The 16th-century Book of Royal Degrees records that Daniel was given Moscow on his father's death in 1263. The principality was transformed into a centralized Russian state in the late 15th century and formally became the Tsardom of Russia in 1547 when Ivan IV was crowned the first Russian tsar.
Daniel, the youngest son of Aleksandr Nevsky, was the first prince of Moscow. The original territory likely encompassed the basin of the upper Moskva River, stretching roughly between the eastern influx of the Gzhelka and the western influx of the Ruza. By the time of Daniel's death, his sons had expanded the principality nearly three-fold to include the entire Moskva River and its tributaries.
Moscow's independence from the Golden Horde was a gradual process. The grand principality refused to acknowledge the khan's suzerainty in several periods, including 1374-1380-1396-1411, and 1414-1416. Ivan III's defeat of the Tatars in 1480 traditionally marks the formal end of Tatar suzerainty. Ivan also refused to recognize any khan as his suzerain and adopted the title of sovereign of all Russia.
The Russian Orthodox Church was central to Moscow's growth. Metropolitan Peter moved his residence to Moscow in 1325 and intended to make it the religious center of Russia; he died there in 1326. His successor Theognostus completed the Dormition Cathedral and canonized Peter in 1339, increasing Moscow's prestige. In 1448, a council of Russian bishops unilaterally chose Jonah as metropolitan, a declaration of autocephaly that was confirmed by the fall of Constantinople in 1453.
The Battle of Kulikovo in 1380 was a Russian victory against the forces of the Mongol warlord Mamai. Prince Dmitry of Moscow assembled troops from across his territories and defeated Mamai's army before Lithuanian reinforcements could arrive. Although Tokhtamysh subsequently sacked Moscow in 1382 and Mongol suzerainty continued, Dmitry gained recognition that the grand princely title and the territories dependent on Vladimir were now a hereditary possession of the princes of Moscow.
Ivan III ruled the Grand Principality of Moscow and is credited with transforming it into a centralized Russian state. He formally annexed Novgorod in 1478 and Tver in 1485, absorbed other appanage principalities, and tripled the size of the Moscow state through wars and diplomacy with Lithuania that ended in 1503. He was the first Muscovite ruler to use the title of tsar in correspondence and adopted the title of sovereign of all Russia. His defeat of the Tatars in 1480 traditionally marks the end of Tatar suzerainty.