Workaway.info and helpx.net are the big websites for volunteering.
In the first world, people have computers and labor is expensive, so volunteering is apparently quite easy. I've met many people who worked their way around Europe hardly spending a euro. You normally have to be able to commit for a month at least to be taken seriously, though.
In the third world this is not the case. Westerners are viewed as having insanely high living standards and local labor is cheap. It would be cheaper to hire somebody in the village to build your school than it would be to coddle some inexperienced college kids to do the same work (at least this is the belief). So yes, most "volunteer" opportunities end up being more like fundraising ploys, asking for huge fees to cover "room and board".
However, despite this difficulty there is a huge demand for help in all sectors, so it is still possible. I volunteered for three weeks in Ghana, teaching at a poor village school. In the same village I met a midwife who was volunteering in the same way, not through a program, just through some connections she had come across. In Senegal, I met a man and he invited me to volunteer teaching an English class, which I do once a month.
Personally, I do not feel in the least bit altruistic in my volunteer work. Of course once I get to know the kids I come to care about them, but my trip is inherently selfish. When I choose to do volunteer, it's because I want to know the people, know the place, know myself in difficult situations. I do good work and help as much as I can during my time, but it is selfish.
Whether I made a difference, or actually helped? Well, if nothing else those kids now know how tiny Ghana is.
PA180349 by
jordan325ic
It took God 6 days to create the world, and me 6 days to paint it. On the 7th day, I rested and drank "Chickbuku Shake Shake International Beer" out of a carton.
As far as actually working for pay, that is more difficult. I do private English tutoring here in Dakar, but it's just enough to cover rent. If you have some sort of desirable speciality AND you speak the local buisiness language fluently AND you can commit to a long stretch of time (1+ year) then you may find something to fund your trip. Otherwise, you're out of luck in the 3rd world. There is no way you can compete with a locals for "unskilled" labor.