Salta has an international airport (SLA) with regular flights from Buenos Aires (around 2 hours). Direct connections to other Argentine cities and some international routes exist but are limited — Buenos Aires is usually the hub.
By bus, Salta is well connected to the rest of Argentina and to neighbouring countries. Long-distance buses are comfortable and a reasonable way to travel. From Salta you can reach Bolivia via the border crossing at Salvador Mazza/Yacuiba, with onward connections to Tarija and beyond. There is also a historic metre-gauge railway line that once ran to Antofagasta in Chile (the "Train to the Clouds" section is the tourist portion), though long-distance rail services in this region have been intermittent in recent years — check current status before planning around them.