Isn't that cool to see? My trainer has 10 dogs (she used to breed labs) and they are ALL like that. They come to classes and help demonstrate and I've seen them do agility and more and they are amazing.
It IS possible to have well trained Yorkies. Loki was a terror when he was a puppy so he and I did lots of training and he can do stays and all of those things (he's iffy with distractions, but that is due to lack of me practicing with him). Anyway, we used all positive reinforcement techniques. I'm not a Cesar Milan fan because while some of what he says is true (exercise, etc.) what he does isn't. (He might say the dog is calm when the dog is visibly stressed, for example) He uses old school techniques that make for good TV but not good training. The real trainers out there (I'm talking the PhD's, the people know have studied it their whole lives) don't agree with him. There are so many better techniques out there that really do work, they just take a lot of effort and repetition.
So many people explain the right way to train better than I ever could. Pick up a book by Pat Miller (Positive Perspectives) or watch "It's Me or the Dog" on Animal Planet with Victoria Stillwell. Also check out
www.whole-dog-journal.com
If you have specific questions I'd be happy to share! I do have a bookcase full of books on positive reinforcement training if you need more suggestions!