It is split about 50/50 among owners if this is done at home or by the veterinarian.
There are pro's and con's to both. If your dog is very patient and sits nicely for you...allowing you plenty of time to reach all areas and not feel rushed, it may be best to do this yourself. However, if your Yorkie just won't stay still for this and is very resistant to having the tool in his or her mouth, it may then be best to leave this for the specialist.
Most owners try this at least 1 time, to see how they feel about it...and how their dog reacts...Then a decision can be made. An owner should not feel intimidated. This is very similar to when humans use a plaque scraper.
Some actually opt to use a human plaque scraper, which can be purchased at any store in the dental care section. However, there are scrapers made specifically for toy sized dogs. This is recommended, since the Yorkie is very small and a scraper for toy breeds will fit easily into their mouth without feeling too overwhelming.
The dog should sit down (and should already be used to having their teeth touched from the daily or weekly tooth brushings). As you carefully scrape each tooth, use clean gauze pads to wipe the plaque from the scraper. You may find that you need to wipe it off several times for each tooth, both front and back. Small pieces of gauze work well, as you can easily toss them aside and use fresh ones as needed.
Since your dog will be trying very hard to behave and sit nicely while you do this, if they make it trough without worming around the entire time, do reward them afterward with lots of happy praise and a yummy treat. Once the teeth are scraped, you should follow up with a brushing. And then of course, with another yummy dog treat to reward your Yorkie for being so good.
A Word of Food & Treats
Long ago, it was thought that feeding a dog dry dog food or hard dog treats was sufficient for cleaning the dog's teeth. We now know that this is not true. No matter which type of food you offer, whether wet or dry, brushing and cleaning is a vital part of caring for a Yorkie.
Offer treats that are created to help maintain good dental hygiene at least 1 time per day. These help remove some plaque and keep jaws strong.
Never think that "a dog's teeth will take care of themselves". It is a myth that a dog will clean its teeth by chewing on things; this only cleans teeth a bit...not enough! To keep your dog healthy, one must understand all dental issues.