Your Yorkie should be bathed once a week with a good quality dog shampoo and rinsed thoroughly.
Start brushing your puppy even though they don't need brushing yet, it gets them used to it. It would be good to get them used to a blow dryer when they are small.
Their toenails should be trimmed regularly, if you are afraid though, take them to a groomer or check with your vet. Most would charge a nominal fee to trim nails.
The hair on their butts, should also be trimmed, as this prevents faeces from becoming caked on, which prevents them from being able to poop. It is a very common problem with longhaired dogs, which can cause impaction if they are unable to poop.
As the hair on their face gets longer, their eyes will get gooey at the corners. This can be prevented by trimming those hairs, but if you want to let it grow out, you will need to clean their eyes regularly. Special wipes are sold for this, but you can wet the areas with a washcloth and lukewarm water and use a fine comb to comb it out.
Brushing their teeth should be started at an early age. This will help to prevent tarter build up, bad breath and gum disease.