General advice for finding volunteer work is to ask at language schools; they usually know of several programs suitable for their students. South American Explorers (SAE) has an online volunteer database and also folders with reports left by foreign volunteers at the SAE clubhouses in Lima and Cuzco.
Both nonprofit and for-profit organizations can arrange volunteer opportunities, if you contact them in advance.
It’s increasingly difficult to obtain residence and work permits for Peru, and likewise to get jobs without a proper work visa. Some jobs teaching English in language schools may not require one, but this is illegal. Occasionally, schools advertise for teachers, but more often, jobs are found by word of mouth. Schools expect you to be a native English speaker, and the pay is low. If you have teaching credentials, so much the better.
American and British schools in Lima sometimes hire teachers of math, biology and other subjects, but usually only if you apply in advance. They pay much better than the language schools, and might possibly be able to help you get a work visa if you want to stay. In Lima, the South American Explorers clubhouse and international cultural centers may have contacts with schools that are looking for teachers.
Most other jobs are obtained by word of mouth (eg bartenders, hostel staff, jungle guides), but the possibilities are limited. There are volunteer organisations that offer internships and short-term job opportunities.
If you’ve ever thought about living and working in Peru, then why not teach English as a foreign language (TEFL)? It could be the key to funding your travels and experiencing new cultures in a totally new way. You don’t need teaching experience or even the ability to speak the local language – although you might learn it while you’re out there.