A computer that’s on the public internet to run it on. While crunching through video and serving it to viewers can be intensive from the computing side, you can get away with pretty meager resources on a simple setup. If you don’t already have a server to run it on you can get a Linode instance for $5/mo that runs it fine. If you worry that you’ll be maxing out the bandwidth or transfer limits allotted to you, then utilize External Storage very affordably (or even free for a certain amount) to serve the files instead.
Here are some hosting providers people have been successful with.
ffmpegv4.1.5 or greater needs to be available on your machine. If you use the quick installer it will try to download a copy of ffmpeg for you if needed. If you’re using Docker, the image already contains it for you. Note: The Snap package of ffmpeg is not compatible with Owncast.