Visitors who wish to get to know Glacier Grey can enter the park at Pehoé, crossing the lake on the catamaran and from there choose one of a few options. You can camp, or stay in the refugio or in the dome tents at Paine Grande, and hike up and back to Glacier Grey in a day, through forests and wildflowers that grow over hidden streams.
Another, more peaceful option (the Paine Grande campsite is quite large, and the refugio there has a bar) is to hike up (about 3.5 hours) with your gear, and spend the night at the Refugio at Glacier Grey. Here you can get up-close and personal with the glacier, or, if you've chosen the dayhike option, have a bowl of steaming squash (or other) soup at lunchtime. Like at all refugios, you take your shoes off before you enter, making this place feel like a cozy cabin.
You can also hike up and then take the boat (about an hour) over to Hostería Grey to spend the night there.