Cairn Terriers are loyal, lively, and intelligent, which should make them easy to train. But because these dogs seem like they need to be on the move constantly, training certain behaviors such as not barking can be challenging. Many say Cairn Terriers are untrainable because they are so stubborn, but the reality is that with the proper training techniques you would be amazed at the many things you can train your terrier to do.
One of the most important things about training a Cairn Terrier is that they need lots of consistency in the training program. You simply can't go about training your pup not to bark on a willy-nilly basis. You have to work at it every day, preferably in several short sessions each day if you want the training to be successful. Anything less will only lead to failure and a much harder time the next time you try to train your pup to be quiet.
There are, of course, going to be times when you want your pup to bark, such as when a stranger comes to the door or he sees someone lurking around outside. But even then, you want your pup to bark in a controlled manner, not going off on a barking jag. The best way to teach your terrier to be quiet is to first teach him to bark on command and while you are doing so, teach him to be quiet on command as well.
Before you start working on training your dog to be quiet, he should have mastered the four command basic commands of 'come', 'sit', 'stay', and 'down'. Not only does this show his ability to master commands, but it will help you while you work to break your pup of his barking habit. By the time you are done, your pup will only bark either when you ask him to or when the situation demands it.
Since this training is all about breaking a bad habit, you really don't need much in the way of supplies. Instead, it will take plenty of time and patience to get the point where your pup learns when it's okay to bark and when it's not. However, you will need a healthy supply of his favorite treats, and a place to train him where you won't be bothering the rest of the house.