The way to travel around South America are busses! You can fly, but it’s usually only affordable within one country, if at all. Interestingly bus fares and bus standards vary widely between countries even if you only take into account tourist busses.
The most important thing you have to learn is to distinguish the classes. There is standard: the usually uncomfortable cramped busses that you find all over Europe. Then there is semicama: giving you a bit more space for the legs and the possibility to lean back you seat by 140dg. Cama: gives you support for your legs and and seat that leans back 160dg (if you ever wanted to learn how business class in a plane feels, this is quite similar).
And the 180dg: it’s the same as cama but your leg support can be adjusted to 180dg.
Argentina has in general the highest standards with clean busses, working toilets that don’t spill their content on the street. Sometimes they even serve real food (all of it contains in some way ham and cheese) and wine. Anyway, you should ask for the food otherwise you can end up on a 24h journey very very hungry. The downside: they are also the most expensive ones.
When they tell you that you get food in Chile be prepared for orange juice and cookies and that’s it. In Bolivia they make it easy: no food. But here you can buy supplies and even a warm dish at every corner. And if they don’t serve you food in Peru they will let the street vendors in the bus selling everything from cheese, meat (chopped from the bone in the bus), jelly, juice, but no coffee :(.
What you have to cope with, when taking the not very touristic busses are the cultural differences most pronounced in Bolivia, where seats are in general stained, people eating rice and fried chicken from there lap and people using the curtains to clean their hands or even worse their noses. Anyway what we never ended up with (and people transport the weirdest stuff) were living animals, not even a pet.
And against the warnings of the German embassy and the constant lack of seat belts in Bolivia and Peru we only felt insecure once. On our last ride from Cusco to Lima the bus driver tried to get home early. Instead of 22h he only needed 19h, 12h of them in the middle of the night through narrow bends next to steep cliffs through the Andes. I rarely slept a minute on this overnight bus.
We also took the train twice but more about that in the articles about Potosi and MachuPicchu.