“Down” can be taught very similarly to “sit.” You can wait for your dog to lie down (beginning in a boring, small room such as a bathroom can help) and capture the behavior by reinforcing your dog with a treat when he lies down, giving him his release cue to stand back up (and encouragement with a lure if needed) and then waiting for him to lie down again. When he is quickly lying down after standing up, you can begin saying “down” right before he does so.
The foundation of training should be based on positive reinforcement. Positive reinforcement is the process of giving a dog (or person!) a reward to encourage the behavior you want, like getting a pay check for going to work. The idea is not to bribe the behavior but to train it using something your dog values. Avoid using punishment such as leash corrections or yelling. Punishment can cause a dog to become confused and unsure about what is being asked of him. It is important to remember that we can’t expect dogs to know what they don’t know – just like you wouldn’t expect a 2-year-old child to know how to tie his shoes. Patience will go a long way in helping your new puppy learn how to behave.
Keep your training sessions short, consistent and always have fun. The key to shaping your puppy's behavior is to start out with very easy commands, continue to build on these successes and apply heaps of repetition. Base your puppy training sessions around trust and mutual respect rather than old school methods based on punishment, avoidance and harsh corrections. In this environment you will find that your puppy loves his training sessions and his confidence will grow with each and every session.
It typically takes 4-6 months for a puppy to be fully house trained, but some puppies may take up to a year. Size can be a predictor. For instance, smaller breeds have smaller bladders and higher metabolisms and require more frequent trips outside. Your puppy's previous living conditions are another predictor. You may find that you need to help your puppy break old habits in order to establish more desirable ones.