Begin at the Paradise Inn. This first section of trail is paved, but don't be misled — it quickly turns to dirt with many steps. Strollers are best left in the car.'
Within less than a quarter mile, arrive at a bridge over picturesque Myrtle Falls, where you have a great photo opportunity. Snap a picture, then continue on.
The trail becomes dirt and rocks here, and while the tread is pretty flat and wide, it can be uneven in places. As you look up ahead, you may glimpse the trail switchbacking up the emerald-green slopes in front of you — yes, you're headed up there.
About three-quarters of a mile in, you'll reach the base of those switchbacks and head up. Take your time and enjoy the ever-improving view of the Tatoosh Range. You'll begin to see the Paradise Inn and Visitors Center as well, and of course, the massif of Rainier looming ever larger.
The "golden gate" that this hike is named for is the viewpoint at the junction with the Skyline Trail. Here, there is a flat spot where you can sit and enjoy the views, but they only improve if you continue up the Skyline Trail. It is possible to create a loop hike with the Skyline Trail in either direction — see WTA's entry for the Golden Gate Loop for more details on this.
If you are satisfied with your hike here, take a rest and head back to the parking lot the way you came.