Your new little puppy is probably going to be full of energy when it first meets you and your family, and will consider you to be new play mates to mess about with. However this is an opportune time for them to learn the rules of their new home and what is acceptable behaviour. Correct consistent training is important from the outset, as not only is training much easier at a young age, but while unwanted behaviour as a small puppy may be a nuisance, as a full grown dog this could be a real problem or even dangerous.
Start your training as soon as your puppy gets home, using the mantra of "reward good behaviour, ignore bad behaviour", so if your puppy chews on a chew toy, make sure you give heaps of praise. With a young puppy you should avoid disciplining with loud noises or physically, as this will make them fear you, simply redirect the behavior - replace the table leg with the chew toy, make sure you play with the chew toy to increase its "value" in your dog's eyes.
Puppies in a litter together, will experience a lot of rough and tumble while playing. This will include learning boundaries by nipping, or gently chewing. Watching a litter of pups playing together, you will notice that if one gets out of hand or over excited, the pup on the receiving end will give a yelp. to tell the offending pup they have overstepped the mark. This can be used of your puppy gets over zealous with you, simply give a yelp, ignore your dog and stop the play session. You should play an interact with your puppy a lot, but puppies should learn from an early age that play does not include teeth.
Training your dog to stop nipping or gnawing can be difficult, and a lot of dog owners struggle with this. Always make sure you have a suitable substitute chew toy to hand to substitute as soon as the unwanted behaviour occurs. Perseverance is required, but they will rapidly learn that if they want to play, it means keeping their teeth to themselves.
Again, always remember to reward good behaviour, so encourage chewing on toys, and be very positive when they do the right thing, so they develop positive habits. Try not to use discipline as shouting or physically disciplining your dog can make the situation worse and reduce their trust in you.
Another annoying behaviour that dogs can develop is jumping, they also have a habit of doing this with muddy paws, when you have just changed into your best clothes for an important outing! Jumping is a natural behaviour for a dog when excited or greeting a friend, so a lot of owners will tolerate this, when they have been away and return as obviously the dog is very pleased to see them, you should however keep in mind, that with dog training consistency is very important, so it would probably be easier to train, that jumping is never allowed.
As with all training, preventing jumping will require persistence, the first rule is to ignore the dog completely until they have calmed down. Simply turn your back on them if they jump at you. Once they are calm and have all paws on the ground, heap praise on them. Your dog will soon learn, that the sooner they reach a state of calm, they will get your full attention (and a treat!). The crucial part of this, is that the whole family must be on board, and behave exactly the same way. It is common for one family member to make the training much harder than necessary, by allowing unwanted behaviours and undermining the hard work of everyone else. To that end, you should instruct all visitors to ignore your dogs until they are calm and settled - though you will find this much easier said than done.
During teething, all puppies with mouth, this occurs at about 12 weeks of age, don't be alarmed if you find their puppy teeth on your floor, as this is the same process as humans losing their milk teeth. Much as human babies can be grouchy during teething, puppies can be pretty unbearable as they will want to chew on anything and everything to ease the painful process. As with biting, you should substitute anything being chewed with a chew toy, any attempt to mouth or chew during play, should result in a firm "no" and the play session should cease. As soon as your puppy starts chewing on a chew toy, they should be rewarded and have praise heaped upon them.
Adolescent dogs, while testing their boundaries will often nip, my youngest border collie went through a nightmare phase of this which made walking across the garden a absolute nightmare! Of course for a dog such as a border collie, this behaviour is fairly natural (nipping at sheep to herd them), and for other dogs it is way for them to push boundaries and investigate their environment - again ignore it, a firm no, and redirect their attention onto something you want them to do.
As ever make sure your dog has plenty of chew toys available, and reward good behaviour.
If you are concerned about your puppy chewing unwanted things while you are away, consider getting a play pen or crate training if not left for too long. This will keep both your dog and your belongings safe while your dog is growing up to be a good member of the household.