If there is one thing that drives shih tzu owners crazy everywhere it's excessive barking. When something sets them off, these little dogs can really get themselves worked up into a lather. If you're not there to stop it, the noise could go on for half an hour. Gentle training of your dog, when kept up, should yield good results.
While its worthwhile to have your shih tzu alert, to warn you when something is out of the ordinary, until they learn what ordinary is from you, there'll be confusion on the matter and a lot of noise. When it's something you don't want them to bark at, very calmly tell them no. When it is ideal praise them for letting you know, and tell them not to bark any more, now that you know what's going on.
Reward training is generally preferred over punitive training, though sometimes you need to get your shih tzu's attention when they're worked up into a bark and this can best be done with a noise maker or spray with a water bottle. You can make a simple noise maker by putting popcorn or beans in a can and then sealing it up.
In addition to the barking, many shih tzu have a bad habit of whining when left alone for any length of time. Exercise is good for keeping this down, but amounts to quite a bit of walking per day. Playing fetch is good exercise and some dogs love it. It is sometimes difficult to get your shih tzu enough exercise every day to curb behavioral problems. About a half-mile walk should be sufficient. Getting two dogs at once can also solve this problem, as long as you make it known that you're the boss of both your Wonder Twins.
When considered from a dog's point of view, many of the actions of humans are incomprehensible much of the time. When it comes to behavioral training, you must be instructional, firm, loving and generally a leader and teacher. You must teach all the humans to not startle a dog that is easily driven by fear. This may be something as simple as yelling or people in hats, but until something they know is good happens, the dogs are going to be worked up.
Perhaps far more troubling for both owner and shih tzu is an unfortunate tendency to engage in fear biting. This is, of course, more common in smaller dogs than large ones, but such behavior is most commonly associated with dogs that have either been poorly socialized as puppies or the victims of verbal or physical abuse.
Having your puppy meet a large variety of people, dogs and situations when they're young encourages them not to be afraid, especially if you're a bit cautious about situations where the dog may be hurt. This doesn't mean snatching your dog up on the street when you see a big dog approach. It means to ask the person the dog is attached to whether they're friendly or not and simply walking on the other side, if not.
If you exhibit your own fear, your shih tzu will pick that up, as they learn best from example. They are also very sensitive to their small size. Fear biting is also commonly seen with fear-induced urination. Keeping your temper at all times, no matter what the dog has just peed on, is instrumental in not making such a delicately tempered dog any worse.
Thankfully this also means that a shih tzu is small enough to be simply picked up and put in a crate to calm down. This sort of behavior is not acceptable, though. If very traumatized, your animal may never snap out of it entirely and will always crave the attention he or she wants but is too afraid to accept. Having words that always calm your dog down or a place it considers safe, will be necessary.