Develop a schedule
The #1 problem with bitey, jumpy [bad] puppies is a lack of rest! Imagine a baby without a nap. Super difficult!
Crate overnight. Crate when you're gone. Crate when you can't supervise. Puppies need more rest... more down-time. Puppies are generally over-stimulated. Puppy behavior gets worse when they haven't had enough rest. So, if your puppy is being difficult, implement a daily schedule with daily naps. Implementing a schedule with nap times solves MANY problems.
Typically, until six months of age, your puppy should be on a schedule of 1-2 hours in the crate for every 1 hour out of the crate. Puppies can easily sleep for 18-20 hours a day. Ideally, you should have two crates: one in a quiet location (away from windows) where your puppy can sleep and gain confidence in your absence, and one in a central area of your home for quick containment.
When your puppy is in its crate, expect calm behavior. This also means that you shouldn't be talking to or engaging with your puppy while it is in its crate. Kids should not be engaging with or teasing your puppy. When your puppy is in its crate, it is expected to be calm, so don't make it harder for your puppy to maintain that calmness. Let a sleeping puppy sleep. Tired puppies bite, jump, and lack patience. What they practice is what they get really good at. When you're home, focus on "quality time" instead of "quantity time".
Control space in the house
Too much freedom is possible. Besides the crate, you can utilize baby gates and a leash inside the house. At all times, your puppy should be "within your sphere of influence". Your puppy needs to be within sight (unless crated in another room). Your puppy can be resting in the crate, back-tied to a doorknob or heavy piece of furniture with a leash, working 1-on-1 with you, or just well supervised (like a toddler would be).
I highly recommend that your puppy wear its leash when you're together in the house, so that you can influence your puppy without needing to approach or grab your puppy. Your puppy can just drag it around. Puppies can learn to just run away from you to avoid doing things, and it becomes a game and an escape. If you chase your puppy, you are teaching your puppy to avoid you. Use the leash to guide your puppy toward you, or away from something else, instead.
Encourage your puppy to go over things and under things. Expose them to as much as possible... noises, people, different ground textures, warmer and colder surfaces, slippery surfaces... the list is endless.
When outside, you can use a 15'-20' long line, and allow your puppy to move freely and explore. Look for "small challenges" (active, exploratory behaviors) to help your puppy develop physically and mentally. Do these things together... go over logs, jump up on rocks, climb stairs... encourage your puppy to engage and to conquer the things it may feel uncomfortable with. And train with food! Get a little treat pouch or fanny pack and take food or treats with you on these excursions.
The first five months of your puppy's life includes the critical socialization period. You will want to positively expose your puppy to as much as you can. Socialization does not mean that your puppy needs to get pummeled at the dog park by over-adrenalized dogs with pushy play styles. Socialization includes seeing, smelling, and hearing other people and distractions. But, if you worry and wait until your puppy has all of its vaccines to take it out in the world, then you'll probably miss this critical socialization period. Get your puppy out and about as often as possible! However, make sure that your puppy is safe! If you find yourself in an unsafe environment, pick up your puppy and get out of there as fast as possible!
You want to be the most valuable being in your puppy's life... not the stranger passing you on the street. You do not want other humans to influence your puppy more than you do. Please deny the privilege for everyone to touch your puppy. I know all too well... it will be hard to say "no" when others approach your incredibly cute, irresistibly adorable, puppy... I say, "No, sorry, my dog is in training" when people try to pet the dogs that I'm walking. Practice keeping your puppy calm even when they see others, rather than allowing others to stimulate, adrenalize, and influence your puppy to make poor choices [ie: jumping, barking, pulling, mouthing, etc].
The video above has a lot of tips! In general, take your puppy out when it gets completely distracted from you, has really high energy, or after long periods of inactivity. Be persistent and consistent. Crate after exercise, then potty after a nap. Take water away a couple of hours before bedtime to help your puppy last through the night.
Avoid on-leash, nose-to-nose interactions with unfamiliar dogs. These interactions are not natural for dogs. If your puppy is on a leash, their freedom, movement, and body language is restricted. Instinctually, these movements are used for communication. If dogs cannot communicate with body language, then they typically feel uncomfortable, unsafe, and trapped [and you do not want to be the person who puts them in this situation]. Without trust in you, dogs resort to barking, growling, and lunging to keep others away (since their initial attempts to move and communicate were futile). This results in the highly undesired "leash reactivity/aggression" problem.
Allow your puppy to engage with other balanced, trusted dogs. Allow loose-leash or off-leash interaction with these types of dogs... do not physically restrain your puppy with a tight leash... allow them to move naturally when greeting another calm, appropriate dog. If you are out walking, and someone else's dog is barking and dragging the owner down the street, do not engage with this dog. Utilize space. You can cross the street or walk "in a bubble" around the dog. Choose another, more polite, attentive, calm, and familiar dog to interact with your puppy. This will not teach your puppy to dislike other humans or dogs; this will teach your puppy that they can trust you to protect them!
Handle your puppy every day... touch their ears, feet, toes, abdomen, raise their tail, look at their teeth, and pick up and bend each leg. Get the puppy acclimated to being on an elevated surface... you can use a picnic table, or a tailgate. And, use food during this training! Feed your puppy food or treats while practicing all of this. We want a calm, attentive puppy. Don't use too much excited praise and talk. Pet them slowly, like a deep massage. Touching your puppy should not always adrenalize your puppy, so try to slow your touch. Pet your puppy in a calmer way. Everything that you do... do it slower.
Chewing, jumping, barking
Puppies need to do these things, it's normal and natural... Provide appropriate toys when you are ready to play. We need to control your puppy's surroundings, and what they have access to... much like you would child-proof your house, you will need to puppy-proof your house. However, if your puppy stole something that you don't want them to have, encourage them to bring it to you. Do not chase them for it. Then you can trade for something more valuable (food) and engage with your puppy for awhile. Do not always "take" from your puppy. You can use containment (like baby gates!) to prevent your puppy from destroying your belongings while they mature.
Interaction is good, but dogs don't just naturally respect children because they are human. Children behave differently than adults... they are loud and energetic, and they are smaller. Adults set boundaries for both dogs and children... which both should respect. However, children don't set boundaries. Either, the adult needs to step in and advocate and train the puppy its boundaries around the children, or, the adult needs to teach the kids how to set boundaries with the puppy, just like the adult did. If time is unstructured, and children are playing rough, the puppy will play rough, but we may not want the puppy to play rough with children. So, crate the puppy, or engage the puppy in an activity (fetch, tug, training with food). Teach both the puppy and the children how to interact appropriately and respectfully.
Puppies are typically over-stimulated. Dogs read our body language and the energy behind it before they ever understand words being said. Don't badger your puppy with voice commands (repeating commands over and over again) when your puppy does not respond. Help your dog understand what you desire, and use food or treats to help train your dog. Food consumption is calming, and food is highly motivating for dogs (because dogs need food to survive). We need to be calm if we expect our dogs to be calm. Model calm behavior.