To visit Tierra del Fuego National Park, your best bet is to fly to Ushuaia and explore the area from there. There are several daily direct flights from Buenos Aires, which is almost 1,500 miles (2,400 km) away—most international travel to Tierra del Fuego does go through Buenos Aires. There are also direct domestic flights from El Calafate and Trelew (near Puerto Madryn).
Check out this 13-day itinerary that takes you down to Ushuaia for trekking and canoeing, loops through El Calafate and the Perito Moreno Glacier and then north to visit Iguazú Falls.
From Buenos Aires
Duration: 3.5 hours, plus travel to/from airports
There are several direct daily flights between Buenos Aires and Tierra del Fuego's capital city, Ushuaia. Flights usually depart from Aeroparque (AEP), Buenos Aires' domestic airport, which is located in the neighborhood of Palermo and is easily accessible by private transfer or taxi. Once you arrive in Ushuaia, the city center is only a quick 15-minute car ride away.
From El Calafate
Duration: 1.5 hours, plus travel to/from airports
Flying from El Calafate to Tierra del Fuego takes less than 2 hours, and both cities are small enough that the airports are very easily accessible. A private transfer to El Calafate Airport will get you there in around 25 minutes.
From Puerto Madryn/Trelew
Duration: 1-hour transfer to Trelew, 2-hour flight
If you're traveling from Puerto Madryn, you'll probably be flying out of Trelew Airport, one hour away. Shuttle buses leave from Puerto Madryn to Trelew every 30 minutes, and private transfers are also available.