At what point will puppies start responding to training/discipline?

We just brought home a 7.5 week old pup and in one week she has already learned to sleep in the crate, **mostly** housetrained, not to nip/bite our arms and shoes, and even how to sit. Pretty amazing how quickly they learn.

If you're doing it right, and in a way the pup understands, the results are almost immediate.

Some hints though: 

Restricted freedom:  If you cannot supervise your pup, confine him/her.  Tether him/her to you with a short lead, restrict access to the whole house-that's setting your pup up to fail.    This will make potty training so much easier.  If you are crate training-the crate is the pup's den.  make it comfortable and inviting.  That's his refuge and where he should be when supervision is not possible.

Discipline:  Think of discipline as setting boundaries that both you and the pup can live with.  Decide now which behaviors now will be acceptable once the pup is an .  If you do not clearly define those behaviors now, you WILL have an dog that thinks they are perfectly fine behaviors. 

Chewing:  Depending upon the breed, chewing/teething is an absolute all stages of life activity.  Start now by encouraging chewing on appropriate items.  Rather than "correct" the pup when it chews on an inappropriate item, simply redirect; place an appropriate chew toy in his mouth.  ALWAYS have at least one or two appropriate chew toys within hands reach, preferably on your person.  This way you can redirect at the exact moment you discover the inappropriate behavior, rather than 30 seconds or 2 minutes later.  By that time the pup has moved on to bigger and better places and things.

Those are just a couple of basic hints, hope they help.

All dogs learn at a different pace.  Most of it is dependant on you.  If you never set the dog up to fail he will not develop bad habits and good habits will become ingrained quickly and early.  He should respond to training immediately but set the bar as low as you can and raise it gradually - as his training progresses and he gains maturity you will continue to see good progress and good responses from him.  If you "test" him, push him too far too fast, set him up to fail..... well then he will appear not to respond to the discpline and training. 
 
Ed's dedinition of "discipline" is excellent.  Never assume that to discipline the puppy you need to correct him.  Make it impossible for him to get it wrong and praise and encourage him for getting it right and he will progress faster, be more reliable and you'll both be happier.  In short, place the onus for getting each step right on yourself, not the dog.

Your puppy has been learning the whole time,,,, the problem is likely that what you thought you were teaching is not what the puppy is learning. 
 
So, clear communication, which means the words and body position need to be identical so the puppy can build a strong association with a specific set of cues and a desired behavior. 
 
Doing the desired behavior needs to result in the puppy getting good stuff.  Attention, pets, a bit of play time, maybe a treat.
 
Repetition is incredibly important for the puppy to develop the ability to understand you.  However, it may seem the puppy has it perfect, then you ask for the behavior some where else, and it appears the puppy knows nothing.  Not so, dogs are situation specific or context bound.  It means that just because you know it in one place, does not mean you will know it in another. 
 
An excellant site with information and suggestions is [linkhttp://www.hollysden.com]www.hollysden.com[/link]
 
Get in a puppy obedience class and then take 2 more classes minimum.  And follow Ed's advice above, darn good stuff.  The management is a key,  if the puppy can not practice bad behavior, it will be less problematic over the dog's life time.

Check out [linkhttp://www.puppyprodigies.org/VideoClips.htm]this website[/link] for video clips of a puppy beginning training to be a service dog at 20 days of age (you read that right).  Now of course training service dogs is sort of a special case and these are folks who's entire job is to do extremely early training of dogs who will wind up being very valuable, but it shows what is possible to accomplish, even in very young puppies. And of course your pup will be over 8 weeks of age when you get him or her, but I wanted to share these video clips because they are pretty amazing.
 
If you use positive methods, you need not worry about waiting until the puppy is old enough to harshly discipline in order to begin training. That is in fact one of the benefits of positive training--you can begin when a puppy is much younger than more punitive trainers would suggest beginning, because training that requires physical corrections is very dangerous for young pups.

If the pup never gets any attention, even eye contact, for jumping up, he will tend not to do it.  You can also train him to "sit" to be greeted, as that is a behavior incompatible with jumping.
I do not "discipline" my dogs.  They get rewarded for good behavior, and I generally redirect, or ignore, bad behavior so that it will extinguish (ever hear of Pavlov and Skinner? []).  Watch the free videos at this site, and you will see the basics:
[linkhttp://www.clickertrainusa.com]www.clickertrainusa.com[/link]
It's never necessary to be harsh or physically correct a young puppy.  If they nip at your hands, you can:
1. Give a "yelp" and remove your attention.
2. Exercise the pup so that he is not as inclined to be looking for things to do with his mouth - it's harder to nip if your tongue is lolling out from being tired.
3. Make sure he has chew toys that are safe. (Kong, Buster Cube, Orbee bones etc.)
4. Avoid pushing or shoving him off - this can be interpreted by the pup as an invitation to play harder, or as aggression, neither of which helps you get a pup to stop nipping.
Read "The Culture Clash" by Jean Donaldson.

Raising a pup is like raising a child.  If you Google on "puppy stages of development" you will get some idea of what they go through.
If you are a first time owner, and afraid of dogs in general, as you posted on another thread, it might be better for you to start your dog-owning career with a stable, calm, well-socialized older dog.  Quite a few of them need homes badly, and if you work with a reliable rescue group, you can get a nice dog.  A good trainer can help by evaluating the dog's temperament for you.  Around here, that would cost you maybe $60-75.

ORIGINAL: spiritdogs

If you are a first time owner, and afraid of dogs in general, as you posted on another thread, it might be better for you to start your dog-owning career with a stable, calm, well-socialized older dog. 

 
A positively excellent idea if I may say so.[]

You should start training right away, and you may see compliance some of the time rather quickly, but IMO it's most realistic not to expect to have a well-behaved angel until the dog is at least 2 years old. Some people may disagree with me... and to be sure there is always that puppy here or there who is housetrained in a day and obedient in a month - that puppy who makes other puppy owners want to jump off a bridge LOL... but most puppies lack the self-control to do what you say every time and never make mistakes. They are the equivalent to children... and teenagers from 12-18 months... and their ability to get ahold of themselves and make good choices is usually not far off from humans of the equivalent age. []

I have some video clips of my uppies being trained and/or showing off their training. One is of Sienna at at 8 - 9 weeks doing "gimme 5", "down" and riding a skateboard. Another is 6 week old puppies going pee in the litter box. One is a skate board lesson at about 6 weeks.
 
[linkhttp://poodlejunction.com/video/index-of-videos.htm]http://poodlejunction.com/video/index-of-videos.htm[/link]