One of the downsides of having a dog with a very short snout is the prevalence of gingivitis and gum disease this tooth formation encourages. In fact, the shih tzu is not unique in this problem, many other dogs with short noses (also called Brachycephalic) are at special risk for gum disease and possible tooth infection or loss.
This problem goes much farther than having a dog with a stinky face or even loosing teeth - tooth infections can actually kill or make your dog very sick, indeed. Even low-level infections from long-term tooth decay can lead to health problems such as decreased immunity and overall vigor.
It is difficult to give your Shih Tzu enough material to chew on that won't cause jaw problems or even crack the teeth you're trying to save. The best course of action is to give your dog a regular tooth brushing and attend to their tartar buildup on a regular basis. Even dogs that are only two or three years old can have enough tartar built up to have the first stages of tooth decay.
The amount of hard tartar that is allowed to build up on a shih tzu's teeth is a good indicator of how much attention you need to pay to the gums, as that's the major reason teeth fall out. If you can scale your dog's teeth yourself, that's good, but most people go to the vet and pay for a professional cleaning just as you might receive at the dentist yourself, except with a higher relative dose of sedatives.
Once the teeth are cleaned off and ready to go, you can use a cloth and an abrasive mixture of baking soda and salt. Essential oils are used to make it palatable for humans, though there are several oils (such as tea tree) that actually do have anti-bacterial properties. You may also purchase an enzymatic toothpaste from your vet, often in exciting flavors for dogs such as poultry and beef.
This may be applied with a small brush, or perhaps least traumatic for your shih tzu, with a damp cloth used for that purpose only, since many dogs are distrustful of anyone with an object in their hand. There are also very handy brushes that fit over the tip of your finger. Whatever is most comfortable for your dog and you. A daily brushing after eating will do wonders for your dogs breath and outlook.
Fleas are another problem that long haired dogs such as shih tzus can have a real problem with. There are still flea treatments on the market, as are collars, though most people are concerned about pesticides in the same environment as their pets and themselves, so many people have gone with sub-dermal flea killer and deterrent.
This should always be given under the care of a vet, as some breeds with sensitive skin (as the shih tzu sometimes has) do not react well to the medications. Also, do not purchase much cheaper versions of these compounds that are sometimes sold at pet stores. They have been known to cause severe (sometimes fatal) reactions in some dogs.