Positive Reinforcement training emphasizes rewarding good behavior over punishing bad behavior. This is good. This is wise. This gets the best results. But it is still inevitable that your dog will do bad behaviors. What are you supposed to do then? Just ignore it and hope it goes away? Well, no, of course not.
Except that, yeah, sometimes you should! If your dog is engaging in bad behavior that you can safely ignore, then that's often the best way to handle it. If your dog is barking at you to get your attention or to demand food or a toy or to be let out of a crate, then your best strategy is to just completely ignore your dog until they've been quiet for a while. No eye contact, no talking to them. Act as if they didn't exist. Once they've figured out the bad behavior isn't getting them anything, they'll eventually stop wasting their energy.
Dogs themselves can be masters of this. Here is a video of my boxer Krypto when he was a wee puppy, trying to see if being a barky little pest will get him the bone that my older girl Derby was chewing on. Other than a slight snark from her when he actually tried to get in and take the bone, all she did was quietly but utterly ignore his obnoxious behavior. It took him almost four minutes to get the message, but eventually he figured out it wasn't going to work and he calmed down. After that, he almost never barked at Derby for anything again.
WHEN IGNORING DOESN'T WORK
A lot of times, just ignoring a behavior isn't an option. If your dog has jumped up on a piece of furniture that you don't allow them on, then ignoring it is the same as giving them permission to misbehave. What to do then?
Well, the first thing to do is “management” - setting your home and lifestyle up so that your dog has a little opportunity to misbehave as possible. Your dog can't jump on your bed if he can't get into your bedroom. He can't jump on guests if he's kept behind a baby gate when they come over. While this might seem like “cheating”, it actually serves a very real training purpose – it keeps your dog from practicing bad behavior and building bad habits. It's not usually enough to fix a problem on its own, but it is an absolutely necessary part of training. Set things up so that your dog only has the opportunity to misbehave when you can be there and are able to do something about it. The rest of the time, set them up so they have no chance to misbehave.
If your dog does misbehave, usually just being more stubborn than your dog is enough to fix the problem in a short period of time. If your dog jumps on the couch and won't respond to you saying “Off”, just calmly (not angrily!) pull him off the couch. If he jumps up again, repeat. Repeat as many times as it takes him to understand that you are more stubborn than he is!
(My mentor, Janine Pierce, likes to say that the best dog trainers are women, because they're naturally bossy. My retort is that men make awesome trainers, because we're stubborn!)
But a very, very important flipside to handling your dog's misbehaviors is that you must be aware and reward your dog when he doesn't misbehave. Did your dog jump on the couch five times and you had to pull him off each time? On the sixth time, did he look like he was thinking about it, but then turned away? Praise the heck out of that little guy! The next day, did he come up to the couch but then just lie down on the floor next to it? That deserves a belly rub!
Remember, good behavior, almost by definition, is easy to ignore. Don't. Notice when your dog is doing the right thing, and reward them for it, and both of your lives will be much easier.