The easiest way in is by air. Presidente Carlos Ibáñez del Campo International Airport, 20 km north of the city, has several flights a day from Santiago (around 3.5 hours direct, longer via Puerto Montt) on LATAM and Sky, plus summer connections to Puerto Natales and, in season, the Falkland Islands. Airport taxis and shared shuttles reach the centre in about twenty minutes.
By bus, the overland route is long but interesting: from Puerto Natales (3 hours) or Ushuaia in Argentine Tierra del Fuego (about 12 hours, with two ferry crossings and a border). There is no direct overland link to the rest of Chile without crossing into Argentina, as the southern ice fields sever the country from Puerto Natales northwards. From Río Gallegos in Argentina, buses run several times a day (around 5 hours).
By sea, small ferries cross the Strait of Magellan to Porvenir and Puerto Williams in Chilean Tierra del Fuego, and the spectacular Navimag ferry runs north to Puerto Montt through the fjords (roughly four days).