I know it's hard at first, but in time I'm sure it will be easier. Like everything, it takes time and a lot of patience to get through it. Here is how I got Henri used to brushing:
First, take Piper into the bathroom with you when you brush your teeth (like Britster mentioned), get her used to being in there if she isn't already and so that she knows that the bathroom means teeth brushing time. Also, Britster made a very good point of getting her used to her lips being messed with by using positive reinforcement and treats.
Next, start by putting a little bit of the doggie toothpaste of your finger and let her lick it off. Make sure to get a flavor she likes, this makes a HUGE difference. Considering how much of a fighter Piper is, you might have to do this for a few days to get her acclimated to the toothpaste.
Once she is used to the toothpaste, put some on the toothbrush and let her lick it off. This will get her used to the toothbrush.
Finally, when you think she is ready, go for it! One thing to remember is that you only need to brush the outside of the teeth, the pup's tongue will move the toothpaste to harder to reach places on its own.
Here is a video that might help:
Also, I find it easier to use a finger brush. It gives more control, especially with how small Yorkies' mouths are.
Henri now actually likes getting his teeth brushed, he rarely fights me on it anymore (he only fights when he is in a mood). I hope this helps and good luck!
