As there are different norms and requirements for different countries, it is difficult to put all these requirements together into one article. Therefore the following article is written as a guideline and additional explanation. In any case this article is no substitute for checking with your local embassy, consulate or local government service to inform for the latest requirements and news regarding travelling to the South American country of interest.
Regulations and requirements do tend to change over time, often due to changing international relationships and alliances. If you are coming from Western European countries, Australia and New Zealand, for most South American countries you will only require a valid passport with at least 6 months left on the passport from the day you enter the country. US citizens however need to acquire a visa for Brazil and Bolivia for instance. For the countries where no visa is required one will receive a tourist visa upon arrival. The tourist visas are obtained on arrival. You will have to fill out an immigration form and will receive a stamp in your passport and the immigration card. Keep your immigration card with your passport and make sure not to lose this. You will have to hand in your immigration card when leaving the country. Your tourist visa will be, depending on the time you have planned in the country, valid for up to 90 days. After 90 days in most countries you will either have to leave the country and come back in or require and exception from an immigrations officer. Keep in mind that it is not allowed to work with a tourist visa. In most countries not even as a volunteer. For several countries a proof of return or onward travel is required on entering the country, even though this often not checked upon entering.
Therefore before travelling get in touch with your embassy, ministry of foreign affairs, governmental travel organization and find out what are the specific requirements regarding your passport and visas. Most governments have websites available with the latest information regarding as well as other destination specific travel guidelines.