Short answers, pulled from the story.
Russian Cossacks expanded from the Ural Mountains to the Pacific Ocean in 57 years, from 1582 to 1639. The river network of portages and connected waterways made this rapid advance possible despite the vast distances involved.
Furs were significantly easier to transport over water than overland, and the river routes connected the major fur gathering centers across Siberia. The network allowed for relatively quick transport between settlements such as Narym, Yeniseysk, and Yakutsk.
Road building in Siberia began in the 1730s, and from the 1760s an overland route from Yekaterinburg to Kyakhta began replacing the rivers for trade. The Trans-Siberian Railway, begun in 1891, and later the Trans-Siberian Highway completed the transition; the highway's Amur stretch was finished in 2013.
By the early 18th century, trappers and traders had collected furs without any effort at sustainable population control, causing a sharp decline in fur-bearing animals across Siberia. In 1913 a ban on sable hunting was introduced specifically to prevent the sable from going extinct.
The routes reached Okhotsk on the Pacific coast, about 5,600 km east of Moscow. Intermediate distances include Tobolsk at roughly 1,800 km, Yeniseysk at about 3,200 km, and Yakutsk at approximately 4,900 km from Moscow.
The Northern Route was used by Russian Pomors, who had navigated the White and Barents Seas since at least the 12th century. It ran from the Gulf of Ob through Mangazeya (1601) and Turukhansk (1607) along the Lower Tunguska to the Vilyuy River and then to Yakutsk, roughly 2,400 km from the Taz Estuary. After about 1700, most trade shifted south and the western portion of this route was largely abandoned.