To get to Los Graciales you first have to get to El Calafate. The journey by road is just over 36 hours, it's quite expensive and inconveniencing unless you're on an extremely tight budget I suggest that you fly from Buenos Aires EZE to El Calalafe international airport.
There are daily flights to El Calafate not just from Buenos Aires but from Ushuaia, Bariloche, Cordoba, and Mendoza as well.
From Buenos Aires to El Calatafe the flight takes about just slightly over 3 hours, At the time I was visiting, the flight cost US$ 300, approx AR$17000. You can check for current prices using apps such as sky scanner.
From El Calatafe
From the airport, there are buses to town that cost AR$ 100.
From the main bus terminus in town, you can buy your bus ticket to Los Graciales for AR$ 800 ( approx US$ 15). The buses usually leave El Calatafe in the morning hours, between 7 to 10 a.m and usually begin the trips back to El Calatafe afternoon.
Duration of travel: The trip takes one and a half hours.