You also want to try to make sure that the local community also benefits from the program. I like that the director specifically addresses this and says they employ locals and that they have a good relationship with the community.
ResponsibleVacation.com
This site is an aggregator for a huge variety of both eco-friendly tours and volunteer trips. It's great if you already know where you want to go because you can search by region/country. With each description they get pretty specific as to how this trip differentiates itself as sustainable instead of just saying "It's green! Trust us!"
You don't really book anything through them directly; if you're interested in a particular trip, they put you in touch with the actual organizers. The majority of the options & tours were out of my backpacker budget, but you can find some more inexpensive alternatives if you look long and hard enough. Honestly it's hit or miss and some info might be inaccurate or misleading.
For example, I found a three week all-inclusive voluntour program in the Maldives with a huge range of dates that was advertised at the time as $1563 for 21 days which works out to about $75 per day (which was already on the higher end of my budget.) But, once I actually started corresponding with the company Rainbow Voluntours via email, a representative told me that specific trip was actually only offered from 10 Aug - 31 Aug (not the range I wanted), limited to 10 people and the cost listed was "starting from" and that I'd have to pay $1800 for that specific week, which upped the daily cost to $85 per day. If I wanted any other date range, which I did, it would cost me $1500 for two weeks and an additional $590 per additional week, so now my daily cost was up to $100/day. I was not happy and really felt like this was a bait-and-switch tactic and no longer had interest in booking anything with them.
But I also found a couple of eco-resorts (keep in mind this is not the western definition of resort) with which I had great experiences. The Paradise Eco-Resort near Siem Reap, Cambodia was exactly as advertised and offers a range of rooms for all budgets from $12 - $45 USD. They are super close to the temples at Ankor Wat, offer a super affordable restaurant on site and offer other local-led tours. The staff is also super helpful and responsive via email.
I also wanted to stay at the TCFD Eco-Logic Resorts for Charity, which was set up to support the Thai Child Development Foundation, but couldn't work it into my schedule. Once I started corresponding with TCFD, I found out the volunteer exchange (work in exchange for free lodging) was different from what was advertised on the responsiblevacation.com site, but everything else was pretty consistent.
I provide these examples so you don't get all excited like I did and start planning out an itinerary based solely on the info on an aggregational website before confirming details like dates and prices with the actual organizations. And on a related note, Google Drive is great for planning, organizing and comparing info. I utilized a spreadsheet in Google Sheets to compare locations, programs & costs and copied and pasted a calendar template into Google Docs to keep my dates straight.
Finally, there were websites that I can only describe as complicated, information chaos like Eco Friendly Vietnam. I mean, the information on this thing literally moves in like 5 different directions and makes me feel like I might have a seizure. Nowhere do they list any kind of pricing, a red flag to me, and their Environment Corner is just general information and travel warnings and I don't see how it relates to their specific trips. I think this is a case, where they are just trying to capitalize on the green travel trend. (You're not supposed to judge a book by it's cover but this is the 21st century so I will judge a business by it's website.)
Thanks to the internet it's both harder and easier than ever to plan your trip. There are so many options that it just comes down to researching the trip that's right for you and best aligns with your values and passions. Hopefully my insight and experience so far helps point you in the right direction. :)