What tools do I need to keep my Shih-tzu properly groomed?  

Hello, the best tools to have are a slicker brush and a greyhound comb (google greyhound combs, they are not for greyhounds as the name suggests.)

Start with the slicker, gently and carefully dont scrape it agaisnt the skin, have a routine and keep to that order so you dont miss any and dont forget groins and armpits and behind ears as these areas matt the most easily. Once you have brushed then go through with the comb, not forgetting the hard to reach areas.

this done every couple of days should keep the coat knot free, use a misting spray either water or a detangle lotion as you go to prevent breakage specially if the coat is very dry.