The eye area, and the face in general, are the hardest parts of grooming simply because you need your dog to sit perfectly still in order to cut away in these delicate areas.
The most important tool? Sharp, snub-nosed scissors. I picked mine up at a holistic pet shop where the owners regularly show their dogs so they had a lot of expertise in grooming and actually cater to people who groom their dogs for show, so they had all the right supplies. However, many pet stores carry grooming equipment. The owners explained to me that the snub-nose is most important because if your pet does move, there is no pointed tip to harm them.
Now I have trained my boys to sit still by using voice commands...speaking gently to them and raising my voice slowly and adding firmness if they continue to squirm around. Now they will lay in my arms or sit quietly on the floor while I groom their face. This method of training requires an inordinate amount of patience (which, thankfully, I have). However, I know people that have little or no patience and the methods they employ are to place the dog on higher ground such as a grooming table, the washing machine, bathroom counter or other place which is high enough that your dog will be afraid to jump. Therefore, there is limited mobility.
I know one person who actually put his dog in a sling that suspends in the air and the dog doesn't move simply because she is petrified of being suspended. Whether this is right or wrong is not for me to say since I haven't actually seen the contraption, but if it works and it doesn't hurt your pet, it should be okay.
Of course, I recommend my method but it's certainly not for everyone. Usually, what works best is a combination of a high table and some voice training. And that is the biggest hurdle you will face.
At first, it's a bit tedious to get the area trimmed neatly because, let's face it, dogs have no patience. Even after some training they'll sit still for a bit but then they have to move around. Unfortunately, until you get the angles right, you'll be trimming and checking and retrimming for a while while your dog loses more and more patience. Sometimes you end up letting them go and realize later that their little faces look a wee bit crooked. But it is practice that makes you better. I've found through my own experience that making little cuts in the fur and taking a bit more time ends up producing a much nicer cut overall because if you make a mistake, you can go back. If you cut too much off with the first snip and you've messed up the angles, it's hard to recut to balance the look of their face.
If your dog's hair is long it's a bit easier as the hair on the side of their nose is growing down and doesn't really require too much trimming. However, it's a lot trickier to attain balance if you've had their face groomed short to match their body.
Grooming the Shih-Tzu's face is not for everyone. Either your dog won't sit still long enough, or you can't even come near them with the scissors, or you don't get the angles right. At the bare minimum, try to just get the areas around the eye so the hair is not touching the eyeball because that is what can lead to eye irritation and infections. For the rest of the face, leave it to a professional groomer.
And if you absolutely cannot do anything with your dog's face, take him or her to the groomer every three weeks for a face touchup.