There are plenty options for cross-country traveling in South America. Most common for longterm travelers is to start in a city and go by bus through the continent. What if you only have a some weeks to discover the continent. Sure, flying is the fastest. To save money one could try to find error fares, if you are not that into airline fare system, air passes can be decent value. find out more about airpasses!
Pura Vida Expedition 