i have a 3 month old puppie, VERY VERY INTERESTED IN PUPPIE THINGS 
chewing, very good at not "going" in the house, will nip at the fingers now and then, digging ….. how old until the puppy will start really catching on what is good and bad? we tell her no with every bad thing and praise her with every good thing and i can tell something are catching on but is there a time (i.e. after 6 months, 12 months, etc.) when the puppy will start learning best?
Dogs do not know "good" from "bad". Good/bad is a human concept and has to do with feelings, as right/wrong is to logic and thinking.
Training is a matter of *conditioning* an animal. Conditioning requires repetition. There is no need to lay a hand on a dog to train him to sit, lie down, shake, and many other actions. He is already capable of doing these things; what you want is to condition him to do them on command. If you want him to sit you merely have in your hand something he wants, his food bowl or anything, but you don’t put it down for him until he calms down and sits there waiting. Then you say "sit" and give the food. After a number of repetitions he will be conditioned to sit whenever you say the word. Additionally, an exuberant puppy will not knock the food or water bowl out of your hand if he is required to sit down first.
Many behaviors can be "learned" at a very early age. My 10-mo old pit bull was sitting on command at 10 wks old. But a dog may not have the attention span for some of the more difficult training until he is 7 or 8 months old. At this time, his earlier training should be reinforced as well.
You should express displeasure anytime he nips, just as his mother or litter mates would have done. What you do depends on how hard he bites. Look straight at him and say "OW!". Turn away and ignore him. If he doesn’t seem to get the message, say ow in a louder, more serious tone. If all else fails you can give him a shake by the scruff of the neck. Digging should be handled similarly. A firm "NO" may do the trick. If he is determined to dig, you will have to take more drastic measures. You provide for him, and he shouldn’t be allowed to destroy your yard. A "NO" and a shake or a slap or a spray of water might be necessary. If he still insists on digging a hole, place a spring-loaded mousetrap or small blown-up balloon in the hole and cover it with a layer of dirt. Hope this helped.
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