When you start your search, try to find a dog whose personality is a good match with yours. If you don’t have a lot of time for consistent training, you may want to avoid a dog who seems to have dominance issues.
With puppies, a good test for this is to roll the puppy onto his back, and gently hold him down. (Showing the belly is a sign of submission for dogs, so this tests how willing he is to submit.) If the puppy gives up immediately without a fight, the dog is submissive natured. A dog who refuses to give up is one which has a more dominant personality. You would probably want a dog which struggles briefly, then gives up.
Watch how the puppy reacts when you release him. Ideally, he should try to “make up” to you by wagging his tail and trying to engage you in play. A dog which wants to continue to “fight” or one who runs or cowers is probably not a good choice.
Play a game with the puppy to find out how alert he is. You can somewhat test his intelligence by trying to teach him to sit. A smart puppy will catch on pretty quickly, but don’t expect miracles. If he seems to be grasping the concept after a few minutes, it’s a positive sign that he’ll be easily trainable.
Once you’ve made your choice, be prepared for the same interruption to your life as you would have with a new baby. I would strongly suggest bringing him home when you have a vacation week or long weekend to help him become acclimated to your home. He’ll need time to learn the rules, and you’ll need to observe him closely for the first few days to find out what areas need work.
Be gentle and patient. Remember that your dog wants to be good, he just doesn’t know what you want him to do. Praise him lavishly when he behaves well. He’ll learn what earns him a treat very quickly and be eager to do those things. Praise is much more effective a training tool than punishment.
You will have occasion to punish him, unfortunately. In doing so, remember that dogs’ understanding of cause-and-effect is pretty weak. Punishment must be IMMEDIATE for any rule-breaking. Even a delay of just a few moments can cause the dog to disassociate what they did with your reaction. Long-term punishments, such as locking him in a cage, don’t work either. He’ll quickly forget what he did, and instead focus on the fact that you’re rejecting him.
Temper any punishment with directing him to do the correct thing, and then praising him for behaving. For example, if you catch him chewing on your shoe, it’s best to tell him “NO!”, take the shoe away, give him one of his own toys, and then praise lavishly when he chews on it.
Once your dog is trained, he will bring you much joy. Good luck on the search for your new friend.