Biting and mouthing
Puppies play using their mouths. Your puppy will want to play with you, meaning that he'll want to bite and mouth your hands. This is rarely aggressive behaviour in pups but if it is not stopped it may become so in adult life. It is very difficult to stop or suppress this behaviour, so the best option is to offer an alternative.
When you go to stroke your puppy, have a toy ready in your hand. When he goes to mouth you, put the toy into his mouth instead. Stroke with one hand, and offer the toy with the other. This way the puppy learns that human attention is nice and can still display his normal chewing behaviour. Vary which hand holds the toy and which does the tickling. You may have to start off with short burst of this training as prolonged attention will cause excitement, leading to nipping.
If you are nipped by your puppy, you must teach it that this is wrong and will stop any social interactions with you. Look him in the eyes and say "OW!" loudly, as if you've been badly hurt. Then ignore him completely, leaving the room if necessary. Only return when he has calmed down, then try the chew toy method again.
You can also discourage nipping by loosely and gently holding his lower jaw between your thumb and first finger when he bites you. Hang on for a few seconds, so that wherever his mouth goes, your hand goes. He'll get bored of this very quickly.
Thirdly, try wearing a pair of thin cotton gloves coated with a nasty taste like bitter apple or sour lemon. This way, he'll work out that hands taste nasty. For this to be successful, your hand must taste bad every time he nips you. The puppy may well learn to distinguish between gloved and un-gloved hands, and continue to mouth the un-gloved hands.
When your puppy jumps on you, he wants attention. Even negative attention such as pushing him off, is attention, so he'll keep on doing it. Instead, you must completely ignore him. When he jumps up:
Once you've taught him to ask for attention in this calm way, be careful not to ignore him when he does ask for it. You must reinforce good behaviour.
If your puppy chews your slippers, or steals a glove, or gnaws on the furniture, what do you do? You immediately focus your attention on him. Even though you may be cross and shouting at him, he's still getting the attention he wants. The answer is to ignore him. If he steals something and you chase him, he knows that stealing leads to a game. Next time, don't chase him. Don't talk to him or make eye contact, leave the room if necessary. He'll soon get bored and realise that this doesn't work. He may even drop the item and come to look for you - praise him if he does this.
Although not really bad behaviour, separation anxiety is still behaviour that can be corrected. Your dog will bond to you and may get distressed when you leave the house. Signs of anxiety are whining, barking, howling, depression, loss of appetite, toilet accidents and self-mutilation (by over-grooming an area, leading to fur loss). Your dog will soon learn to recognise the signs that you are about to go out, and his tension will build during this period. Within the first few minutes of your departure, he will bark and whine, then resort to either destroying anything he can, or to more passive behaviour such as depression.
To correct this, you have to teach your dog that you will be coming back - for all he knows, he might never see you again. Start by just leaving the room the dog is in, and moving to a different room, leaving the dog behind. Try settling him with a favourite toy or a biscuit. After a very short time, a minute or so, return to your dog and praise him. Start gradually increasing the time you leave him for. Then start actually leaving the house, again for a very short period at first, gradually building up the time you are away, always praising the dog on your return.
If you have a very destructive dog, it may be a good idea to get him a pen or cage to sleep in while you are away. Get him accustomed to it before you leave him in it. When he knows it is his bed, and is comfortable in it, you can start training him to sleep in it while you are away. Start off by shutting him in at night. When you put him in, he'll realise that he will be alone for a while, but will know that you will come back. When he's happy with this, you can start leaving him in the cage while you leave the house, again taking the same steps as above. Always make sure that the cage is an appropriate size for the dog you own.