As stated above, this trail is not for everyone. Dogs are not permitted. The trail (see pictures below) requires some climbing over angled rocks. If you are not careful you could be seriously injured. Speak to a member of the ranger staff in the Visitor Center to discuss your suitability for the hike.
While the entire hike is only ~4 miles, it can take five hours because of the rough terrain and large number of hikers on busy days. If you are hiking on a weekend, get there early (9AM or earlier) if you want a more pleasurable experience.
Begin by walking south from the parking lot. You will pass a white building with picnic tables in front that serves food and drink, followed by a set of bathrooms before getting to the Visitor's Center. Cross the bridge at the Visitor's center to access the tow path and continue to walk south until you reach signs for the Great Falls Overlook/Olmstead Bridges. Make a right and cross the bridges on your way out to the Overlook (~0.25mi). The Overlook provides great views of the Falls. Return to the tow path the same way you came.
Continue on the tow path until you reach signs for the Billy Goat Trail A on your right (~0.35 miles from Overlook) . You will see a bridge crossing the canal to your left when you get to the trail head. Heed the warning signs and continue.
In many places along the trail, there is no discernible path. Follow the blue markers (see picture below) on the trees and rocks to stay on course. You should see these markers roughly every 50 yards or so. There are many places along the hike to take a break and enjoy the view of the river. Several pictures found below highlight what to expect along the path in terms of terrain. It is worth looking them over ahead of time to know what you are getting into.
Eventually you will conquer the rough terrain and make your way to the tow path. Make a left to head back to the Visitor's Center and enjoy the flat towpath along the Canal.