Their motto pretty much describes how it works. You use the Ecosia search engine (https://www.ecosia.org/) and they use the money earned from the ads accompanying each search to plant trees all over the world, more than 62 million so far!
They have extensions for Firefox and Chrome so you can set it as the default search or just have it available as an icon and mobile apps in Google Play and the Apple AppStore.
I would expect that for Opera, the Chrome extension should work since I believe Opera is now based on Chromium, which also powers Chrome.