Article the third [Amendment I]
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.
"Separation of Church and State" is inferred from the first section by interpretation and, as you say, legal precedent.
Basically (and basically as I understand it), the first part says that the federal government is secular - it cannot force a religious context into law (as it has on several occasions nonetheless - "under god", "in god we trust", and so on). The second part says that religion, otherwise, cannot be regulated by law.
No religion in laws, no laws for religion.
That is what is termed "Separation of Church and State". There is no direct statement to this effect in the Constitution, but this is the overall interpretation of the First Amendment with respect to the relationship between religion and federal government. So, in effect, it is loosely written into the Bill of Rights (more accurately).
This is why state or local mandates allowing the Decalogue, prayers, whatnot in Federal courthouses, public schools, and any other Federal buildings can be overridden by application of this amendment. Newdow has a strong case against the "under god" inserted into the Pledge of Allegiance in 1954 since it was done through Congressional act. Despite its supposedly "secular" deity reference, it is still an invocation of religious significance in a Federal form. Uh-uh. That violates the First Amendment.
As long as ignorant people keep spouting lies about our nation as a "Christian nation" and our laws being based upon the Decalogue, and as long as our "Reborn Christian" president remains in office, I feel that we are at peril of completely losing the veracity of the First Amendment, in part or in general.
Kuroyume