Being considerate seems to be something people are having more and more trouble with these days.  So, just a little kindness to others on the trail will be greatly appreciated by the vast majority of the people out there.  When we're talking hiking, there are two general areas of how to be considerate, and they both fall under the idea of trail etiquette.

The first one is what do you do when you come across another party on the trail.  If you're like me, the vast majority of your hiking will be on trails that are limited to only hikers.  This is the easiest situation as nobody is going to be moving fast enough to cause injury.  When you come across another hiker, the downhill hikers should offer to yield to the uphill hiker.  More often than not, the uphill hiker will say to come on down, taking it as an excuse for a short break.  There are times where this may not be optional, when the hikers are in the middle of a difficult and narrow section of trail, but in general, if possible it should be offered.

On multi-use trails, you need to remember that horses always have the right of way.  Everyone yields to horses.  They are big, they can spook easily, and they can be dangerous.  Just stop as soon as you can, step off the side of the trail, preferably downhill, and let them by.  Bikes are the other thing you're likely to see on trails.  In the case of bikes, they should yield to hikers.  That said, if they're going downhill, they may not be able to stop quickly enough, so be aware when you're approaching blind corners.  There's also the possibility of encountering motor vehicles like ATVs and snowmobiles.  They generally should give you the right of way, but a little courtesy and stepping off to the side of the trail when they come by will make life easier for everyone.

The second area is noise.  When I was a kid, shouting and screaming was the biggest issue for noise.  Maybe someone got a whistle and blew it.  Children are like that, and they still do that.  Ideally you should keep your talking down to a conversational level so only those close to you can hear you, and encourage your children to do so too.  With the advent of portable Bluetooth speakers we're now getting a lot more music in the woods.  This can be more of an issue.  Music is a personal preference, and people can feel passionate for and against specific songs and artists.  If you are wanting to hike with music, please keep the volume down so that only you can hear it.  Ideally, use headphones so only you can hear it.  Hearing someone else's music for extended periods of time while hiking, especially if they're hiking the same direction at a similar pace, really can degrade the experience for the other hikers.

Overall though, the biggest thing you can do is be kind to the other people on the trail.  Be encouraging if they look like they're struggling.  Keep the talk to trail related things like the conditions ahead, or how far you are from the peak.  If someone doesn't want to talk, a polite "morning" type greeting in passing is more than enough.  If you don't want to talk, acknowledge greetings, and keep going.  Doing that, and following the other 6 principles of Leave No Trace, you will be doing your part to make the wilderness a better place.