I've been at Jatun Sacha for 3 months via i-to-i and will go back for a year to work for another organization. You can go via a tour-operator like i-to-i, lead adventures and so on or arrange everything yourself. There are opportunities in teaching, nursing, conservation work and from time to time tourism. A paid job is way harder and almost impossible to find.

It probably depends on whether you can support yourself or you need to be paid. If you have your own funds, you could probably try directly contacting the volunteer organizers at the Charles Darwin Research Station. Here is the website: http://www.darwinfoundation.org/english/pages/interna.php?txtCodiInfo=63 I really wanted to stay and volunteer, but my trip there was only 2 weeks.

The "Fundación Jatun Sacha" (www.jatunsacha.org) has a volunteer programm with a station on the Galapagos Island San Christóbal.