In The National Security Strategy of the United States of America
(September 2002), it states, "As a matter of common sense and
self-defense, America will act against such emerging threats before
they are fully formed."

How does this notion of prevention (or possibly preemtion) violate
international law?

I'm looking for a set of specific international laws to justify the argument.

The international community frowns upon preemptive strikes.  By doing
so, the U.S. has become the aggressor.

It's a vague statement.  In theory, it could mean the US will enforce
the terms of various cease-fire and other agreements that will prevent
known or likely enemies from becoming worse problems (like the UN
failed to do in Iraq).  Legality would then rest on who has the
authority to enforce a specific agreement.

Or it could mean the US is going to beat the heck out of anyone with a
broken tail light.  It's just not a specific enough statement to go
on.

"Preemptive strike" is a vague term  - and a subjective one -  but
there has been much written about it.  Generally, it is felt to mean
attacking prior to an obvious and immediate threat of attack (no
Western film etiquette about the good guy waiting for the bad guy to
draw first).  The 1967 Israeli preemptive strike in the face of the
Egypt's mobilizing forces fits this qualification.

But the quotation in the question does not, saying that the US will
not wait that long, striking at an earlier stage.  Under these terms,
Kennedy would/could have attacked in the Cuban Missile Crisis.

International Law is also vague, since the definition of terms is open
to interpretation.  As I remember, the discussion after 2001 or after
the above statement went back to an incident in the War of 1812, when
the US attacked a ship that had not opened hostilities.  It was just
there, and its presence suggested that it could (my weak recollection
of the scenario).

On this level - or subject - International Law is not LAW but only a
statement of intent or of good will.  Law presupposes a higher
authority that can enforce it.  In International Relations, "Might is
Right."  If the UN had the "might", there are lots of conflicts in the
last decades that it should have settled, but  only resolutions were
issued.
And it is subjective in practice because there does not exist a police
element to enforce it.  Israel is in breach of many UN resolutions,
but nothing has been undertaken to enforce them, but in other
conflicts, the UN has mobilized troops.

The UN Charter (  http://www.un.org/aboutun/charter/  ) is the
International Agreement on the subject, but it is only LAW if there is
an authority to enforce it.

The "bush doctrine" is, at best, in a murky area.  Article 51 of the
UN charter permits military action in self defense, but only in case
of actual attack.  The charter is silent on preemptive strikes.

There is thought to be such an inherent right, existing in customary
international law.  However, the "Webster formulation" (named for
Daniel Webster, its author) of that right grants that a nation may
make a preemptive strike, so long as "necessity of that self-defense
is instant, overwhelming, and leaving no choice of means, and no
moment for deliberation."  This is a pretty tough standard to meet.
Moreover, as the ICJ discussed in the Nuclear Weapons Case (paragraph
41), there is a requirement of proportionality: the response must be
only equal to the threat.  None of the United States's actions in the
past few years seem to meet these tests.

On the other hand, there is also some discussion that, since the above
are merely interpretations of customary international law, the Bush
Doctrine reflects a changing international perception of that custom,
and the Doctrine iteself is now becoming customary international law.