Please, it would be so helpful if somebody steps up and tell me the way to do it.
If you press the "Send to Simulator" button in the Marlowe Playground, there is a "Download JSON" button for downloading your contract in Core Marlowe JSON format. That JSON-format contract can be run using the
In order to run your contract, you'll also need to create a JSON file specifying the initial state of the contract: here are instructions for creating that file. Here is a step-by-step example for actually running a contract on a Cardanon network. Before running your own contract on the network, you might want to run one of the examples first.
Although it is technically possible to run Marlowe contracts on mainnet, the Marlowe validator script has not completed an audit yet, so it is safest to just use a testnet.