2 ways to get there - either take Going-To-The-Sun road from the western entrance to the eastern entrance of the park, then take the road toward Babb until you see the turnoff for Many Glacier. Or, take Highway 2 from Columbia Falls, MT all the way around to Browning, then take the road toward the St. Mary entrance of the park. Instead of going into the park, turn right and follow the directions to Babb, taking the turnoff to the Many Glacier area of the park.
Always have clothing for both warm and cold weather, because even in the summertime, it can still snow or hail up in the higher elevations of the park.
This photo was taken during a mid-July sunrise on the shores of Swiftcurrent Lake, with the Many Glacier Hotel behind me, at Glacier National Park, Montana. It was very chilly that morning (normal, actually) and the clouds were awesome.