This question has to do with something called the Great Consonant
Shift (aka Grimm?s Law), which occurred in Europe a long time ago. The
sounds of the consonants in the Common Germanic shifted systematically
from the Indo-European.

For example,
p -> f  (pater -> father)
t -> th (triple -> three)
k -> h  (cornet -> horn)
b -> p  (bacillus -> peg)
d -> t  (decimal -> ten)
g -> k  (grain -> corn)

I realize that the shift may have taken centuries to complete, but is
there a generally accepted explanation of HOW such an extraordinary
phenomenon might have occurred? (I?m trying to imagine Germanic
ancestors sitting around the fire, many centuries B.C., and suddenly
proclaiming, ?Let?s not say pater anymore. Instead, let?s say
father.?)

Specifically, don?t know, but perhaps linked to the dissolution of
?High German?. The related phenomenon of ?rotating vowels? especially
in the North of US has I believe been quite extensively studied. Very
few hits on Goog for ?rotating vowels? but quite a lot for ?vowel
rotation?. I leave to you.

Best

I think it's pretty impressive that this is the same Grimm of Fairy Tale Fame. 

Language shifts like that do usually happen slowly, over time.
Sometimes they happen quickly. Either a particular way of saying
something is easier (eg, "a napple" becoming "an apple") or one way
becomes more socailly acceptable (based on economics, personality,
what have you.)  Living in "ubran US" as I do now, I can think of two
very annoying examples. First: more and more people are saying
"dubbaya" rather than "double-you" for the letter "W". The other that
drives me simple bonkers is "aks" in place of "ask," as is "can I aks
you you a question." The funny thing about the latter is that in old
English "aksan" was a pefectly legitmate word.

What's really changed is that we now have much better methods of
communication, which in turn have made necessary standarization in
language. Things like dictionaries have both desriptive function, in
that they tell you what a word means, but also a proscriptive
function, that tell one how to say the word, how it's spelled, and
what it means. That would be the closest to a bunch of people sitting
around and deciding "Hey, lets say it this way..." Even so, there are
still influences based on national/ regional/ city dialects, and
things can still shift over time.

For those interested, a good link to Grimm's Law is at 
http://www.finucane.de/grimm.htm

"Sound change" as described on Wikipedia:

http://en.wikipedia.org/wiki/Sound_change