Visit the Pool tab and select "Add pool":
Re-use the name of the pool and the Sync Core URL that you also used on the stage site. If the "Machine name" doesn't match, the content won't be delivered. Give the site a unique name.
If you're connecting the same site to multiple pools, re-use the site identifier if possible. If you're using the same Sync Core for multiple sites, make sure each connected site has a unique name. Otherwise, you can just call it "Production".
After hitting Save, you will be redirected to the export page for the pool. Wait until it has finished before you continue:
You will see a success message once it's finished:
If you see any errors here, you probably entered an incorrect Sync Core URL. In that case re-enter the correct URL and wait for the export to finish.
Further information regarding exporting Pools via the Configuration Management could be found within the section Deploy Configuration.