There is just one "front country" campground in Glacier Bay, and it's located near the main dock and reached via a trail running about a quarter-mile to the south.
The 33-site campground features a bear-proof food cache; a fire-pit with firewood, and; a warming shelter located in a very scenic setting along the shore. Though it's a walk-in campground, there are wheelbarrows you can borrow to haul your gear down the trail.
Even though the stay here is free, you still must obtain a campground permit and attend a 30-minute orientation at the visitor center. Cooking and eating are only allowed in the intertidal zone (the area on the beach between the high and low tide lines).
There are no facilities for vehicle camping or RVs in Glacier Bay National Park (sites, hookups, dump station, etc.), although there are efforts to build at least one RV campground in nearby Gustavus.
Of course, there also are millions of acres that you can pitch a tent on. Some paddlers well-suited for the climate -- rain is frequent, cool temperatures are the norm -- comfortable traveling in bear country, and knowledgeable about tides head out for a week or more via kayak or canoe.
Paddlers can head out either directly from Barlett's Cove and head to the nearby Beardslee Islands, or be shuttled farther into the park via the day cruise ship. Making reservations for a rental kayak and the daily tour boat is recommended well in advance. Guided day and overnight kayak trips also are available.
For details on permits, outfitters, and requirements for kayakers, check out this page on the park's website.
While the park offers acres and acres open to backpacking, there are no established hiking trails for you to follow. As a result, you'll have to bushwhack at times and find your own way.