Use Positive Reinforcement
Scolding dogs does not work. Because of how their short-term memory works (they can only recall specific events for about two minutes), they are unlikely to make the connection between your being angry and the couch cushion they chewed up two hours ago. Rescue dogs might be particularly insecure, so avoid yelling at or punishing your dog at all costs.
A highly effective training method that has become popular in recent years is positive reinforcement of good behaviors, and preventing or ignoring unwanted behaviors. For example, If your dog is destructive when left alone or is not housebroken, use positive reinforcement and crate train him or her rather than just getting angry every time he or she does something you could have prevented.
Give Them Their Space
Speaking of crates, dogs crave a comfy space of their own where they get to just lie around and be left alone -- you know, like you and the couch. Pick an area in your house that is calm with little traffic, no drafts, and no bright lights or rumbling noises from a fridge or AC unit, and make it a cozy doggie chill zone. When your dog is in that space, do not disturb, touch, or otherwise bother him or her. If you need your dog, call him or her to you. Never send your dog to that space as punishment. Having a space to retreat to when needed will help your pooch balance his or her mood and adjust to the new home.
Remember That Training Is an Ongoing Exercise
Some dogs pick up tricks faster than others, but don't expect them to get it right away, especially if you have never trained a dog before. Obedience school is a very worthwhile investment, both for your dog and for yourself, so you can learn more about how to encourage the behaviors you want, and curtail those you don't.
Of course, training and obedience are something you practice day in and day out with your dog, long after any classes end. Especially for more advanced training like "stay" and coming when called (every single time), expect it to take months of repeatedly encouraging those behaviors before your dog gets it.
Establish Boundaries and Rules
Make some ground rules regarding important sleeping and eating behaviors, and areas in your home your dog is or is not allowed -- and stick to them! Your rescue dog may have prior bad habits, and is likely to test his or her boundaries at first.
For instance, if you never want your dog to bug you while you're eating, never feed him or her at the table. Just once is enough for your dog to realize when you're sitting at the table, you might share some delicious human food if he or she begs. If you are not consistently enforcing your house rules, your dog will never know when you are serious.
Set a Schedule and Stick to It
Dogs crave routine. It helps avoid destructive behaviors and accidents in the home. If they know when their morning, afternoon, and evening walks will be, they are better able to remain calm and hold it. You might need to loop in a dog walker to stay to schedule, but that expense can help prevent many potential problems with your dog.
Get Some Exercise
A tired dog is a good dog. Especially if your puppy is younger or going through a teenage phase, you'll need long walks or runs in a dog park every day, rain or shine. Depending on his or her size, a healthy, active dog might need two or three hours of playtime and walks a day. You need to be able to commit to that amount of time with your dog, or hire a dog walker or make use of a doggie day care while you're at work.