If you're a particularly adventurous hiker, you might find yourself on slopes steep enough that you need to use your hands to keep yourself safe and steady. That's pretty much the definition of scrambling, a type of low-grade climbing that occupies a fuzzy area between hiking and actual climbing.
Unless you happen to rock climb in addition to your hiking, your definition of "scrambling" will probably be a lot less technical than what a climber would describe with the same term. That's only a problem if you and someone else are comparing trail notes and the term scrambling comes up -- so make sure to establish a common frame of reference before committing to any hike that involves "a bit of scrambling" (or "a bit of exposure").
Stewart Green, Guide to Climbing, offers great advice on scrambling for climbers. Hikers with the appropriate skill set (and trip plan) should follow that advice -- but you'll also have a couple of additional concerns that climbers might not have to worry about: Finding, and then managing, the route back down. Then there's the extra traffic to worry about.
Getting Back Down
Climbers usually have the option of rappelling back down what they just climbed up, or taking another descent route entirely. But as a hiker, you're far more likely to be making a round trip. Scrambling down is significantly harder than going up, because it's hard to see your next handholds and footholds below you -- so be very wary of getting yourself up something that you cannot safely descend on the way back.
Unfortunately, there's no magic bullet to solve the problem if you're already up and can't safely get back down. Next time, pay closer attention and consider the potential consequences as you ascend -- but in the meantime, you'll just have to try and work out the way back down for yourself. Your options include looking for a safer descent route, finding an alternate route the avoids the scramble entirely, hiking out to an alternate trailhead or road, or asking for a rescue. If anybody else is within shouting distance, they might be able to help you spot a better way down from their own perspective.
(Signaling for a rescue you don't really need is officially a very bad thing; but if you really do need a rescue, signaling for help before the situation becomes critical is a good idea.)
Where Did I Come From Again?
There's also the additional wrinkle of finding your original route on the way back down. Again, it's much easier to gauge which general path is easier on the way up -- so you want to descend by that route, too, if you can -- unless you can spot an easier alternative. Trying to descend without carefully marking the start of the downward route is a recipe for ending up in rock-climbing (or for a hiker, life-threatening) territory by mistake.
Just as looking behind you periodically can help keep you from getting lost on the trail, it's also one of the best ways to make sure you remember where to start the trip back down. Once you're up, pay close attention to what the route you took looks like from the top.
Take a few steps back and scan the area you just came from. Are there any landmarks that make it obvious where the way back down begins? Is there anything nearby that you might confuse them with? Do whatever you have to do to remember where you should start back down, whether that means taking a photograph with a digital camera, sighting off landmarks, or even building a small cairn to mark the descent point.
If you're on a heavily-traveled trail, the extra traffic makes it easier to figure out the established ascent/descent route. But it also brings hazards of its own. On particularly popular scrambles -- say, the upper slopes of Flattop Mountain in Southcentral Alaska -- you can literally get stuck in a traffic jam. Sometimes it's a jam of people all going in one direction; sometimes it's people trying to go both up and down on the same route.
A little consideration goes a long way toward fixing this. Whoever can most safely step aside and let the other person pass in the opposite direction should do so. If you're in a traffic jam of hikers all going the same direction, don't tailgate -- and try not to wait directly beneath anyone. If they drop their water bottle or kick down a loose rock, it's going to be headed straight at you.
If you are that person who drops or kicks something off the slope, follow the climber convention of letting others know by yelling "Rock!" continuously until the object is no longer a hazard: "Rock! Rock! Rock! Rock!" If you hear someone else yelling that, keep your head down and get out of the way as best you can. A Nalgene bouncing downhill can hurt, and surprisingly small rocks can do a lot worse.
But in this case? The views are worth it.