Train
Daily direct flights from Moscow take 6 hours. There are also connections once a week to/from Khabarovsk and Vladivostok.
Sea
During summer there are twice-monthly sailings by ship and more frequent hydrofoils between Yakutsk and the port Ust-Kut. Note that if it takes only 4 and a half days to sail to Yakutsk, the journey in the opposite direction, which is against the current, takes a whole week.