Before I share the details, it should be quickly known that:
1.) Palouse Falls is worth the visit. I drove over 4 hours from Seattle and was not disappointed.
2.) This report is divided into 2 parts. The North part where everyone visits and the South part where hardly anyone goes.
3.) Leave your flipflops BEHIND!!! Make sure to bring sneakers/hiking shoes instead.
Palouse North:
This place is not for long hikes and never-ending trails. In fact, this isn't your typical state park. Think more of a city park with a viewing area (but don't be discouraged, read on). After you exit the various highways and access roads to reach the park, you'll reach the first of two parking areas: an upper lot on the right which is used for overflow parking and a paved lot below which is inside the park itself. Remember to pay the $10 fee (or buy a $30 Discover Pass ahead of time for a year. This will come in handy if you're visiting a few more state parks).
The official park is rather small. It entails a grassy lawn that hosts about a dozen camp sites and several picnic shelters - no different than the average neighborhood park found in any city. This area is perfect for families & groups to spread out for lunch. There's no trouble spotting the falls. There's a primary viewing area attached to the main section of the park and another viewpoint to the right of the park that provides a slightly higher outlook.
However, this is not what people come for.
Start walking along the trails to the left of the park (as if you're facing the falls) and it won't be long before large red signs warn you that off-park trails are dangerous and to proceed at your own risk. Flipflops are NOT recommended. Follow the trail furthest on the left that hugs the railroad track. This will take you down a hillside and drop off into a ravine where the Palouse River runs (5-10 min from the park to the ravine) The ravine is bordered by a towering ridge to the right and the river that rushes through rocks and boulders to your left. The river creates sort of a mini-falls a small pool in which one can easily swim or wade. This alone is a spot worth relaxing, sunbathing or simply hanging out in.
Afterwards, follow the wall of rock. The trail may fade at times but still trek forward and you'll soon find yourself atop the falls. The trail becomes narrow enough where a misstep from too many wilderness selfies will land you in the river or over a cliff. This is also the point where people, brave or dumb, will embark on an even narrower path to the bottom of the falls. It is steep, it is treacherous and it is not for people who merely want to take a selfie with a waterfall behind them. You'll notice the vast number of people who stay above the falls versus the few who go down below. Some selfies simply aren't worth it. Enjoy the what's already around you in the ravine and the heart-dropping cliffs over which you can dangle your feet and enjoy the company of your mate(s).
Palouse South
Away from the families and tourists lies a trail that leads you downriver. The trail begins at the upper viewpoint that is furthest to the right of the park (facing the falls). The moment you step away from the lookout shelter, the State Parks system will warn you with a large red sign that trails beyond that point are a hazard and you'll have to flip the bill if they come rescue you. Trails past this point aren't nearly as hazardous as the ones leading to the bottom of the falls. Make sure you're wearing shoes and knee-high socks or pants. Otherwise you'll end up with tumbleweed & thistles scratching your skin all afternoon.
This trail will hug the railroad track and lead you down a hillside of those sharp, jagged rocks that are often seen around rail line. The trail runs along a ridge that provides a panoramic view of both the falls and river. You'll quickly notice a different trail on a ridge below and second-guess yourself, "Did I miss a turn?" You did not. Keep on trekking as the trail leads further away from the falls downstream. The trail goes through some flat areas which are great for pitching a tent overnight and enjoying the stars. You'll reach another hillside that leads down. But instead of traversing rocks, you'll have to crisscross through tumbleweed and all sorts of bristle-like bushes that are unpleasant on the skin.
But it's worth the discomfort.
It won't take long until you'll find yourself on the bank of the Palouse River, hidden and out of sight from everyone. You'll be tucked away in a canyon that is reminiscent of something you'll find in Utah or Yosemite. The river runs gently so that one can wade across or simply play in. It's also a perfect spot for seclusion, photos and enjoying the company of your loved one in privacy.