In most American cities we say "subway". "Metro" is used in Washington, DC, but people will understand if you say "subway". "Metro" may be used in other American cities as well, but my subway experience is mostly limited to the mid-Atlantic and northeastern USA. In Boston it's called the "T", short for MBTA, or Massachusetts Bay Transportation Authority. In some cities the subway is known by an acronym. In SanFrancisco it's called BART, for Bay Area Rapid Transit.