curl is the quickest way to poke Ethereum mainnet without pulling in a library. It's handy for a fast sanity check that your key works, for reproducing a bug report with the exact bytes that hit the node, and for wiring RPC calls into a shell script or CI step. The JSON-RPC protocol runs over a single verb: every call is an HTTP POST carrying Content-Type: application/json, with the method and params in the body. Your key lives in the URL path, so the endpoint is https://ethereum.therpc.io/YOUR_API_KEY and there's nothing else to configure.
The key in the path is the default, but you can also pass it as Authorization: Bearer YOUR_API_KEY if you'd rather keep it out of the URL and out of access logs. Either way, the request itself stays the same: a POST with Content-Type: application/json. A GET or a missing content type will be rejected before it reaches Ethereum.