Aerolineas Argentinas has daily flights to/from Bariloche,Buenos Aires and Ushuaia. LAN also flies on Monday, Wednesday, and Friday from Buenos Aires. On-line booking and e-tickets are available. During peak season, flights are usually fully booked with tourist groups. Make sure you book your flight well in advance.
There are also charter flights between Puerto Natales and El Calafate operated by DAP. These flights from the tiny airport of Puerto Natales can be very scenic and let you cross the Andes in about 90 minutes and no road travel hassle which however in right doses is something not to be missed in Patagonia.
The only other possibility is to arrive by bus. But this means that you will spend quite some time in the bus on rough roads. Due to the dirty streets, especially when it rains, views from buses vanish fast...
A quite remarkable trip is the bus connection between El Calafate and Bariloche along Ruta 40. It is mainly operated for the benefit of tourists by the Agency Chaltentravel directly only the Calafate-Perito Moreno stage, since people of Calafate and Bariloche have very small ties between each other, which does not sound strange after you have made the journey and seen the state of the road.
Views, if the weather is good, are in places stunning, especially between Calafate and Perito Moreno city, less between Perito Moreno and Bariloche. You must however be prepared for a long 10+ hours for 2 1/2 days and rough trip in a small van. If you are not the kind of person who enjoys slow changes in the landscape and the beauty of lonely places, do not attempt this trip or you will regret it. Of course, if you really like this sort of thing, you will never forget the trip.
The bus trip will let you pass and most likely stay and enjoy through El Chalten and give an opportunity to stay in Perito Moreno from where you can organise a long ride to visit the "Cueva de las manos pintadas".