By bus
Extensive and fairly reliable, can take a lot of time and be very crowded.
By train
Rail service is extensive throughout the region but when you get off the main lines it slows down considerably. The major problem is that since the northeast is connected with the rest of China by a few main lines, long-distance tickets to other places in China past this bottleneck are few and far between, especially sleeper tickets.
The three province capitals of Harbin, Changchun and Shenyang can be reached by direct train from most major cities in the country, only from distant places will a shift of trains in eg Beijing be needed. Other cities in the region has connections from Beijing but not too much from other places.
Northeast China can be entered from Russia via the train from Vladivostok to Harbin. This is a very slow train doing the not very long journey in 35 hours. This train is not much used, you will have to wait long hours in strange places, and crossing the border is a mess. Another option from Russia is there more well-travelled route from Irkutsk to Harbin. It is also possible to go by train from North Korea to the region.