One of the most common reasons for giving away a dog is that they’re destructive and/or not house trained. It’s true that living with a poorly-trained dog is a nightmare, but no dog should be given away because of a human’s failure to train them.
I don’t believe there’s any such thing as an untrained dog. Dogs are trained by their humans, whether for the better or worse, whether the human is consciously attempting to train them or not. Dogs react to their surroundings, and they learn from their experiences.
For instance, if a human pets their puppy every time the puppy jumps on them, that pup is being trained that jumping results in a reward. When that puppy grows up, that behavior will be less cute, and will result in scratches. If it’s a large breed, the dog may also knock people over. The owner usually doesn’t understand why the dog won’t stop jumping, failing to realize that the owner is the reason the dog jumps.
In the same way, if a human takes a dog outside after it pees in the house, the dog may think being taken outside is a result of peeing in the house, and may not understand that it should be peeing outside. It is the owner’s responsibility to take the dog out often enough that it won’t need to pee inside, and to praise it when it shows the desired behavior.
It’s important that dogs be trained not only for human convenience, but also for their own safety. A dog that is not trained to stay or come may put itself in dangerous situations in the event it slips out of a collar, house, or yard. When Belle was a puppy, she escaped through the door as I came home, and ran towards a busy road. Thankfully, we had been working on “come” and she ran towards me as soon as I gave the command. (Yes, the next thing we worked on was training her not to run outside.)
Lastly, training is important because without training, dogs get bored. Dogs (especially the more intelligent breeds, in my experience) display destructive behaviors if they’re not being mentally stimulated. Don’t fall into the trap of thinking that your dog has mastered basic obedience and is now done. Training is and should be a lifelong process. Reinforce training often, and move on to more advanced training when your dog is ready for it.
Basic obedience may include: no, sit, lay down, shake, roll over, come, heel, and stay.
Advanced obedience may include: fetch, get it, drop it, guard, stay (for longer periods or while in another room), go (name a place), hush, services for owners with disabilities, and silent hand signal commands.
Training should be a positive experience for both dog and owner. Most dogs love to please, and a well-trained dog is much easier to manage and will make the owner’s life easier. There are lots of free websites with training tips, or you could always seek out some in-person help if you’re not comfortable training at first.
P.S. I think the best place to get training supplies like halters, clickers, and treats is Chewy.com. They have free 1-2 day shipping on orders over $49. (If you click this link and buy a product, I will make a commission at no additional cost to you.)