Start with the basics. For most trainers, the “basics” are sit, lie down, stay, and come. Although many owners start with the sit command, consider beginning your training by teaching your pet to come to you. This is perhaps the most useful command when it comes to keeping your dog out of harm’s way, and it’s one of the easiest commands for a dog to master. Simply catch your dog in the act of coming toward you and say the word “come” as you offer him praise. You can also practice this command with a long lead in your backyard or other outdoor space.
To start training your dog to “settle,” leash her up and take a seat. Step on the leash so your dog has only enough room to sit, stand, and turn around, but not stray from your side. Then, wait. Your dog may be excited at first, and try to jump up on your lap or run around the room. Let her figure out that she can’t go anywhere. Once she settles down on her own, say “yes!” and give her a treat.
Remember that training begins from the day your new dog comes home. It can be tempting to coddle him for the first week or so to try to make up for the time he spent in the shelter. Don't do it! If you allow your shelter dog to engage in certain behaviors when you first bring him home, such as getting up on the sofa, eliminating on the carpet or chewing on table legs, it will be much harder to train him to stop doing those things later. 

From there, start your schedule of feeding, toileting and play/exercise. From Day One, your dog will need family time and brief periods of solitary confinement. Don’t give in and comfort him if he whines when left alone. Instead, give him attention for good behavior, such as chewing on a toy or resting quietly (Source: Preparing Your Home For A New Dog).
Socialization should begin as soon as you get your puppy and often this means at 7 weeks of age. Puppies naturally accept new people, other species and introduction to new situations during the socialization period which occurs between 7 and 14 to 16 weeks of age. This period provides an opportunity for a myriad of introductions that will provide positive memories that last a life time. Puppies are eager, exploratory and uninhibited during this period and it is important to take advantage of this enthusiasm. Be sure to protect your puppy during this period and ensure that all experiences are positive, fun and not fear evoking.

Likewise, if you have a special place you’d like the dog to stay when she needs to be out of the way of household activities, take her there. This is where you can finally let her off-leash. That place can be where her bed is, or a spot in the corner of the living room where you want her to lie, or her crate. By letting her off the leash here, you are telling her, “This is yours.” Don’t be surprised if she immediately decides to settle down and ignore the family for a while. This doesn’t mean she hates her new home. It means that she has found her place in it.

Some dogs are fearful and when they are exposed to frightening situations, they need to have your reassurance that everything is going to be okay. Gradual exposure to new situations is the best approach. If your dog is afraid of loud noises, start with moderate situations, staying right beside your pet, and increase the exposure giving lots of affection and reassurance, but don’t stress your dog unnecessarily. Overexposure to fearful situations can lead to phobias. Dogs become phobic when they are left alone, victimized by abusive humans or other animals, or neglected by their owners. Giving them reassurance and the best possible care with lots of love and attention increases the odds of having a well adjusted dog.
Expect your dog to break the rules frequently in the beginning. He is not being stubborn or difficult. Dogs have a hard time generalizing, which means that something he learns in the living room will have to be learned all over again in the kitchen and again in the bedroom. It's easy to get frustrated when you feel like he should understand already, but he still doesn't. It helps to have a sense of humor. It can take 30-50 or more perfect repetitions before a dog truly "gets" a command.
Killing and eating: From an evolutionary standpoint, dogs don’t see a massive distinction between beginning to feed and an animal dying—once the prey is no longer fighting or fleeing, eating begins. Therefore, we often see dogs practice the application of a clean dispatch via pressure or the “grab and shake” with toys, ropes, or other items they find.
If you ever become frustrated with training your puppy, don’t get angry with him. Just quietly end the session and try again later in the day. Many dogs become nervous and will stop paying attention to their trainers if they are yelled at. They can become scared of training and decide that following directions is not for them. Stay calm and relaxed so that your puppy will learn in a positive environment.
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