How do natural gas heaters work?
They burn the natural gas like any other gas burner.
“Natural gas” is primarily methane, so it produces less carbon dioxide per energy unit release than other hydrocarbons. It is not a different kind of fossil fuel resource, with the exception that it can be generated by anaerobic processes from waste materials much more quickly than petroleum or coal.
See also https://www.aga.org/natural-gas-heating-systems for a detailed description of natural gas heating systems.