All of mine are bathed in the kitchen sick with the sprayer. Yorkies have a lifelong of grooming so you need to build an excellent foundation from the very beginning.
Here are my suggestions:
1. Lay out all of your supplies ahead of time. Towels, shampoo, conditioner, brush, comb, blowdryer, scissors.........
2. I like to put a hand towel in the bottom of the sick so they do not slide around and feel secure. Other have suggested a sink mat and that would would very well too.
3. In the beginning I always kept their harness on while bathing. It allowed be better control while washing.
4. I always start at the head and wet with a washcloth. Wipe the eyes and around the mouth. I then shampoo the head and work my way back to the tail.
5. Using the sprayer I start at the back of the head and work my way to the tail and underneath with the water. Once they are wet all over I apply the shampoo. If you add a little water to the shampoo bottle it lathers up better and you can work quicker.
6. Make sure that you keep one hand on the puppy at all. Other have had experiences of their puppy jumping out of the sink and breaking a leg. Be very careful!
7. Once the shampoo is rinse you can then condition.
8. I like to place the towel that I use to dry on top of the table or my wash machine to then groom. Make sure that all of your grooming tools are laid out ahead of time.
9. Comb out knots first.
10. I always blow dry too. At first I always used a low setting and worked quickly.
*Most importantly be sure to make it a habit to touch and feel between the paws and all over their body. It is also best to always make it a habit to groom in the same spot. Use treats and calm voice to reassure as you follow the entire process.
Mimimomo sells some nice brushes that are reasonable. She also sells other grooming supplies. She is a member her on YT. Just do a member search.
toplinepet.com