I believe Burgess Falls is actually a series of waterfalls on the Falling Water River. It was a waterfall experience that impressed us so much that it once made our Top 10 USA Waterfalls List.
That said, the name generally refers to only the largest of the waterfalls, which has an unusual shape (almost reminiscent of a smaller version of Union Falls in Yellowstone National Park). Julie and I saw four noticeable waterfalls in a short stretch of the river, which were immediately downstream from a dam that formed Lake Burgess.
There were two trails that led from the car park to the top of the last waterfall. The trail that hugged the river most of the way was about 3/4-mile each way (or 1.5 miles round trip). The alternate trail was on what seemed to be an old road (now a maintenance road), and this one cut straight to the top of the last waterfall bypassing all the other waterfalls en route. I'd imagine this alternate trail would be a little quicker than the riverside trail only because there would be fewer stops. It's possible to make a loop out of this hike using both of these trails in either direction though we happened to do each trail in an out-and-back manner over two visits.
According to a map sign at the car park, the very first waterfall was very close to the car park and it was called the Cascades. This one consisted of very tiny drops cascading (possibly 10ft) and spanning the width of the river in an uneven fashion.
Barely 100ft downhill along the riverside trail, we got to the second waterfall, which was called First Falls as it was the first major waterfall we saw (if we didn't count the Cascades). This one was said to drop some 30ft. There were some concrete and metallic remnants behind the lookout for this waterfall, and I believe they were once part of a flume that was the penstock of an old hydroelectric scheme.
Roughly 0.3 miles further down the riverside trail, we reached a lookout platform for the third waterfall, which was called Middle Falls. The platform gave us top down views of the front of this 60ft cascade, which was very photogenic given its width and lacy appearance. I don't think there was a safe way to get down into the gorge and closer to the falls, but we felt the view from the platform was adequate anyways.
Finally, at about 0.75 miles from the trailhead, we reached the lookout platform for the last waterfall, which was called Big Falls. However, I've also seen the name Burgess Falls refer to just this waterfall alone. This 136ft waterfall was unusual in that it seemed to drop over a protruding wall giving the appearance that it had two walls facing away from each other. Although I've seen photos where the Falling Water River had enough flow to cover the entire wall of Burgess Falls, there was much less water during our visit so it appeared to us as two separate waterfalls. Most of the water tended to fall over the south facing part of the drop, which also was the side most visible without having to wade in the river.
While I'm sure the viewing experience from the overlook would be adequate for most people, we also took the steep trail that descended towards the base of the falls. A signpost stated that this trail was strenuous, but I'd argue that it only got dicey once we got towards the bottom of the descent past the covered stairs. The reason was that mist from the falls tended to moisten and muddy both the rocks and the trail itself, making footing down there precariously slippery and prone to injury with a misstep and tumble. We definitely had to exercise some caution (even using our hands and the sit and scoot maneuver where we weren't too sure whether we could keep our balance).
It was also possible to reach the top of the waterfall just before the stairs. However, there were no guardrails so we also had to be careful not to stray too close to the cliff edge.
During our visit in late October 2012, Burgess Falls State Park opened at 8am and closed half-hour before sunset (which was around 5:30pm). I'd say the best time to take photos would be right around opening time since the waterfall would be completely in shadow. We showed up at around 8:40am and the sun's rays already started to pierce over the the uppermost tip of the falls thereby blowing out long exposure photos. Had we shown up any later, we would've been looking against the sun from the waterfall's base.
Conversely, we also showed up in the late afternoon (around 4:15pm), but we were definitely in a rush to do our exploring before the ranger would close the gate. I guess it was a good thing because it motivated us to make a second trip the following morning (which we just described above). In the afternoon, the sun hit only one face of the falls while left the other face in shadow. Perhaps the sun's backlighting might have been more favorable in the early afternoon when both sides of the falls would be lit up while also producing faint rainbows.
Burgess Falls was said to be named after a Revolutionary War vet named Tom Burgess whose family ran a mill powered by the Falling Water River.
We stayed in Cookeville so we'll describe the directions from there.
On the western end of Cookeville along the I-40, take the exit for Hwy 135 (there are signs indicating for you to take this exit). Head south on the Hwy 135 for about 8.3 miles (veer left at a fork in about 4.7 miles from the freeway). Just as you cross the bridge over the Falling Water River, the turnoff for Burgess Falls State Park is on the right. Follow this spur road another 0.3 miles to the large car park at its end.