In OBS, you add a Chroma key filter to your webcam source. Configure it so that it replaces the green background with transparency.
Then add the image you want as background as media source. Put the webcam source above the image source in the sources list, so your webcam image overlays the image. See also https://www.google.com/search?q=obs+green+screen First search result is a Video from Elgato, should explain it well.
I did this, but I can see the image through my video stream, like I'm partially transparent, even though the opacity of the video's set to full. How do I make the video completely overlay the image so there's no ghost image?
@whitehusky, it might be a matter of the Chroma Key's setting for Similarity. You have to experiment a bit to get the correct value... Too low means that some of the green around you is not transparent (ie. a green halo around your head), while too high means that you will become a bit transparent yourself. Please keep in mind that the correct value might change during the day depending on the changing light that reaches both you and the green screen trough the windows, or changing artificial light.