You can fly to Key West from several major airports. Delta airlines runs jet service from Atlanta (ATL) via Orlando (MCO) to Key West (EYW). Also, a small airline, Florida Coastal Air flies from Ft. Lauderdale (FLL) to Key West and Marathon (MTH).
Amtrak will take you as far south as Miami, and from there you can take the Keys Shuttle to the Florida Keys or Key West.
From MIA Airport, take LeJeune Road south to 836 West. Take the Florida Turnpike south toward Key West. The Turnpike ends at US 1 in Florida City. Follow U.S. 1 south to the Florida Keys.
Once you're in the Florida Keys US 1 becomes the Overseas Highway and is marked with little green mile markers. They begin in Florida City at 127 which is the distance to Key West.