The thing about dog training is that there are so many different methods to "fix" the same situations. The best thing to for someone to do is learn EVERYTHING then apply what works best for you and your dog, store the rest in the back of your head though since you may need it at a later date.
My personal training mantra, especially for puppies is "Interrupt, Redirect & Praise". I use this to fix just about every naughty puppy behavior. lol If the puppy is doing something wrong, I 'interrupt' with a loud "AHT!" or "uh uh!", figure out what I'd rather the puppy be doing instead(redirect), and then praise it once it is doing the better behavior. Though I do have to modify it somewhat when training my deaf dogs, instead of the sound interruption, I sign "stop".. then go on to redirect them in appropriate behavior. I cut and edited the following from another similar post about Guarding Behavior.
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If a dog is growling about something, he/she is telling you that they are uncomfortable in the situation. You need to make them more comfortable.
If they're growling and guarding that means that they're scared their "prize" is going to be stolen from them. You end up reinforcing their fear, if you take it away by force or tease them by sticking your hands in their face or dish.
Here's the best method that I've found to work with guarding behavior. Starting with her kibble. Stand by her dish with a handful of the tastiest treats. Then while she's eating, randomly drop one in every couple of seconds. Her behavior will tell you how often you will need to do this; ie days, weeks or months. When she starts getting happy with you being around her kibble and waiting for a treat then you can move to the next step.
Place only a couple pieces of kibble in her dish, when she eats them all and looks up, then you pick up her dish and treat her(YUMMY treats!).. make sure to do both at the same time. Repeat as neccessary. After she gets comfortable with this step you can add more kibble, but pick up the dish before she's done. REMEMBER TO TREAT at the same time.
You want her to learn that she gets GOOD things when she gives up her "prizes".
Then during day to day things, you should keep kibble or treats in your pocket or in an easy to reach place. If the puppy has something she shouldn't, call her over, offer the treat as you say "drop" or "give"(whatever you want). Pretty soon she'll realise that she'll get something tastier or more fun in exchange.
You can also work on this with toys & bones once she is at this point. Call her or walk over to her for her treat, tell her "drop", give her her treat.. then give her the toy/bone back! She learns that "drop" doesn't always mean she never gets it back.
(This method works great for recalls too! Call dog, treat, then release her back for playtime. They learn that "come" doesn't always mean the end of fun.)
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As far as puppy nipping, I personally do allow my dogs to mouth my hands in order to learn bite inhibition. I teach them from the beginning that we are big wussies and can't handle the same mouthing as another dog would. Its quite comical, especially with my deaf dogs since they can't hear the "YELP!"(training deaf dogs makes you realise how much a dog relies and responds to just body language! lol).
So I'll have my hand in their mouth and as soon as I feel teeth then I jump up, yelp and ignore them for 30 seconds to a minute or so. Totally keeping my back and head turned away in dramatic body language, they learn pretty quick that they can't play with me if they're going to be too rough.
The reason that I do this is because Mojo was taught not to mouth at all and learned horrible bite inhibition. So when I get grabbed by accident by him, it HURTS!!! The others are all more gentle and careful since I taught them bite inhibition as puppies. Again, to each their own, this is just my personal experience.
Good luck and have fun in the puppy classes, they are great! I still bring my dogs to obedience classes occasionally for the much needed distractions and socialization even though I can train them myself at home.