Are visas needed to visit Brazile, Peru, or Chile?

You need to have a passport for the country you are a citizen of, and go to the embassies or consulates for all the countries you plan to visit. They will stamp your passport with a visa that’s valid for entry for up to some number of months, and valid to stay there for some number of months after that. You may be able to mail your passport, but if the embassy or consulate is close by, you’re better off taking your passport in person and waiting. There will almost certainly be embassies for these countries in the capital of your country, and may be consulates in other major cities. Some smaller countries don’t have their own consulates, but will have “consular sections” in consulates of countries they’re friendly with. But before you do any of this, if you’re using a travel agent to arrange your itinerary, ask your travel agent.

The cruise company should take care of all the visa stuff you need while cruising. Not sure about the side trips, but I didn’t need one when I went to Guatemala.

If you are are a US citizen, you qualify for visa waiver with these countries. As you’ll notice from that link, the ones you’ve listed are not on there, so yes you’ll need visas. You may just need it for Peru if the cruise covers the ones that are part of the trip already as @Judi suggests.

You do need a visa for Brazil.

You do not need a visa for Peru.

You do not need a visa for Chile.

Call the cruise line.

EEEK! I linked you to the visa waiver program for people entering USA not exiting. Sorry about that oversight. Ignore my answer and read @bob_.‘s

It changes from time to time. To be sure you are covered, check with the state department and the travel bureau of the country at all times.