There are no direct commercial flights from outside of Africa at the moment. Most airlines flying into Juba leave from Cairo (Egypt), Addis Ababa (Ethiopia), Entebbe (Uganda), Nairobi (Kenya), and Khartoum (Sudan), from whence you should be able to arrange flights to and from Europe, Asia, or the Americas.
South Sudan has a single railway line that runs from Sudan’s northern border to Wau. There were services between Wau and Babanosa before independence, with train links to Khartoum. However, as of 2014, there are no regular passenger services; fact, the whole Sudanese rail network has ceased operations. However, sporadic and non-scheduled trains may still operate, so contact the Sudan Railways Corporation for additional information.