Get there by 10AM on weekends if you want a good shot of getting a table and parking. Also, check out the website to read other advice and warnings before you make the trip. I had spotty cell phone reception with an IPhone 4GS. However, my Nike running App, I used it to track distances, worked brilliantly.
Begin at the Visitor's Center and get a map. They are larger and easier to read then the 8.5x11 versions on the web. The people in the Visitor's Center are very friendly so ask them if you have any reservations about the trail. Locate signs for the River Trail on the side of the Visitor Center opposite the parking lot. Generally speaking, the trails are pretty well signed, so you should not get lost. It may be difficult to walk a dog or take small children on the trail due to the rocks and plentiful tree roots. However, it still may be worth it to try and turn around if the trail becomes too challenging. Talk to the park staff to get a recommendation.
Take the opportunity to stop off at the overlooks on your left as you begin the trail. They provide great views of the Falls and river and provide great photo opportunities. As you enter the forest, follow the green boxes on the trees to follow the trail as it can be ambiguous at times. There are lots of pretty views along the River Trail, so take your time and enjoy them.
After Cow Hoof Rock the trail bends inward towards the woods. The River trail ends somewhat abruptly, as you will come to a set of signs near two sections of wooden fence. You can simply turn back if you want to redo the River Trail, or as suggested here you can hike back on another trail. We suggest you try the Matildaville Trail, as it provides a nice walk through the forest with different scenery. It is a little bit more pleasant than the Old Carriage Road. Note that all three options are about the same in distance and are easily navigated using the map.
If you choose to walk the Matildaville Trail on the way back, make a right at the signs and fence sections to walk on the Ridge Trail. You will be on this for about 0.3 miles. You will pass a sign for Old Carriage Road and shortly after you will see the Matildaville sign. Make a right. You are greeted with a couple of large downhill slopes. Note that these would be uphill if you started on the Matildaville trail. The trail is very pretty and takes you through the forest. There is very nice shade, which is great in the summer. Simply follow the signs back to the Visitor Center (1.3 miles).
I do not recommend you try to run this trail because of the rocks and tree roots that protrude from the ground. It would be very easy to trip.