South America Border Crossing
Border crossing in South America is very straightforward. After landing at your destination by plane you'll be given a tourist visa with a time of stay. This is usually three months (90 days). You can leave the country at any time during those 90 days and can do so either at the country's border crossing or by taking a plane and fly to another country.
Each country has different official crossing points at their border. When leaving a country you present yourself at customs with your passport. Depending on the crowd this can take from 5 minutes up to 5 hours. Getting there early is the message. They check your credentials, scrutinize your pretty face and with a poetic gesture they stamp your passport with an exit stamp.
You cross the border on foot (sometimes by bus or boat depending where your are) and at the country of arrival you undergo the same treatment. You should get a 90 day tourist visa.
Note: I was only granted 30 days when I entered Bolivia coming from Peru. You can get the full 90 days by presenting yourself at Migraciones in La Paz with your passport and claiming your rights for a full stay. Other than that I've never had any problems crossing borders from Venezuela, Colombia, Ecuador, Peru, Brazil, Paraguay, Argentina and Chile.
Border crossing by plane is not at all adventurous. When leaving a country officials will give you an exit stamp before you enter your departure gate. On the plane you'll be provided with a landing card. At your final destination officials will check both your landing card and your passport, give you an entry stamp of 90 days and hand over your passport with a big smile.
That's it! Enjoy your stay!