The most important considerations for training are ensuring the dog's safety, preventing the habit of aggressive behavior, and of course, housetraining. For all other Yorkie training techniques, there are several extremely good books on the market.
Housetraining any puppy can seem like a difficult and time-consuming process requiring the utmost of your attention and patience. True, it is not unusual for it to take most of the puppy's first year of life to become reliably housetrained. However, it can be incredibly easy if you just follow the basics. So don't give up, because if you remain consistent with the training described below, you will eventually be rewarded with a well-behaved Yorkie companion.
Successful housetraining begins with the institution of a regular feeding schedule. Four meals a day at say, 8am, 1pm, 5pm and 9pm. Do not waver from your chosen schedule once you have adopted it. After each meal, once the puppy has eaten its fill, take it outside and repeat the command "Go potty!" until it relieves itself. Then praise and/or reward the puppy.
Follow the same procedure every time the puppy wakes up, too. This includes getting up early enough in the morning to take the puppy outside before it has a chance to eliminate in its crate. For the first few months, this will mean you and your puppy will be watching the sunrise together every morning. This is admittedly quite a commitment, but it is probably the most important "magic bullet" to successful house training. That's because a Yorkie puppy is quite small, and its GI system is even smaller. An eight-hour night is a long time to expect them to "hold it" with their tiny equipment. Please don't ask them to wait for you to sleep late too!
Until the puppy is six months old, it should not be allowed to run freely throughout your house unless it is under your direct supervision. If you cannot pay strict attention to what your puppy is doing, keep it in a crate or pen. Or you can put it on a leash and tie the other end to your belt, so you will know when it starts to do its little pre-potty dance, at which point you should immediately take it outside and repeatedly give the command "Go potty!" until it relieves itself. Then praise and/or reward the puppy.
For a more comprehensive description of these and other successful housebreaking methods, please refer to Donna Malone's How Do I Housebreak My Dog? manual.