what are the requirements of US Citizenship?

If your parents are both US Citizens AND are married:

"A child born abroad to two U.S. citizen parents acquires U.S. citizenship at birth under section 301(c) of the Immigration and Nationality Act (INA). One of the parents MUST have resided in the U.S. prior to the child's birth. No specific period of time for such prior residence is required."

See http://travel.state.gov/law/info/info_609.html for specific details.

(If they are not married or if only one is a citizen, then the residence rules change quite a bit and proofs required may change, but in general you are probably a citizen at birth. You can find more at the same link.)

The Supreme Court has defined "two" types of citizen.

One is naturalized, those who have gone through a process prescribed by law to become a citizen. They were not a citizen and then they beca,e a citizen. These are not "born" citizens.

The second is "born" which means someone who is a citizen at the time of his/her birth. It has divided the born category into two types: those born in the US or its incorporated possessions, which the 14th amendment covers: " All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside. "

And anyone as in your example, who is born outside the US is a born citizen but not by reason of the 14th amendment. The only distinction made in the "non-14th amendment" citizens is that Congress can control the terms under which their citizenship is granted; it is not automatic that you are citizen at birth by the amendment, but instead it is automatic by law. For example, requiring that your parents have resided in the US. The court has held that the Congress has the power to make laws that would not unreasonably take away citizenship if you are not a 14th amendment citizen. For example you can lose your citizenship in some situations if you never come to live in the US up to a certain age. It allows the residence requirement for example.

But because you become a citizen at birth, it has made no other distinction in law, and for the operation of laws it has only two classes of citizen: born and naturalized.

It has never defined "natural born" citizen and has never made any distinction between native born or natural born or born citizens in any ruling (except as to 14th amendment), in every ruling it has made no distinction and has used the terms native born, natural born and born interchangeably, sometimes in the same decision.

While it's a good idea to register your birth at an embassy or consulate, it is not a requirement to obtaining citizenship, it is an acknowledgment or proof of citizenship.

If you ran for President in such a case it is sure that debate would rage about your eligibility. But the court hasn't ever ruled on that clause and as I noted has made no distinction in any of the rulings it has made. No one knows what it would say if a case ever arrived of that sort, all we can say is they don't seem to have made a distinction so far.

John McCain was born, not just on a military base but in the Panama Canal Zone (which no longer exists) which was defined as an organized territory under the sovereignty of the US.

A US military base is not part of the US when in a foreign land; Guantanamo is not US territory in that sense, it is precisely because it's not US territory that it can be used without the constitution applying to what the government does there...

So it might be that he is a 14th Amendment citizen, the Court has not ever rules on this question, but his birth to two US citizens definitely made him a citizen at birth (natural born citizen) either way.