I want to make one thing clear when discussing religion in America--there is no such constitutional clause calling for separation of church and state. This "separation" was not even a notion that they were even considering when drafting the Constitution, much less when they came out with the final draft. If you have a beef with religion, that's your prerogative, but please, don't invoke this fictitious legalism into the discussion.
The origin of the phrase "separation of church and state" comes not from the Constitutional Convention or even the eighteenth century, but from the Danbury Letters written by Thomas Jefferson in 1802. And just so we put the phrase "separation of church and state" into context, the Danbury Baptists were seeking aid from Jefferson for religious disestablishment in Connecticut because the Baptists hated being bullied around by the Congregationalists (i.e., the state-officiated religious establishment for CT). In response, Jefferson subsequently disappointed when he said that he would not intervene because he did not want to intervene in states' rights issues. Even if that bit of history is not to your liking, you run into an even bigger issue: Jefferson had nothing to do with the drafting of the Constitution. As a matter of fact, during this time period, he was an ambassador in France. As bright of a man as Jefferson was for his time, he had nothing to do with the Constitution whatsoever, thereby rendering the Danbury Letters, as well as Jefferson's opinion on the matter, as irrelevant for acquiring original intent of the drafters of the Constitution.
In addition, the phrase "separation of church and state" made its way in 19th-century politics, but it wasn't used by secularists who wanted to do away with religion. It was actually used by Protestants as an anti-Catholic measure. They wanted religion to be separate from politics, but they only wanted it to be applicable to the Catholics. In short, the Protestants, and the Presbyterians in particular, wanted their misinterpretation of the law to be used to keep the Catholics out of politics. This usage also makes sense from a historical context since 1) militant atheism wasn't prevalent until the latter half of the twentieth century, and 2) anti-Catholic sentiment was rampant in America up until around the 1960s.
From the standpoint of the Supreme Court, the phrase "separation between church and state" made its first appearance in Reynolds v. United States (1879). However, the phrase was not used for about another 70 years, when it formally entered the Constitutional lexicon during the case of Everson v. Board of Education (1947). Justice Hugo Black, who used the phrase in his majority ruling, was anti-Catholic. All of this context makes the ruling all the more interesting. In spite of Black being anti-Catholic, in spite of the fact he used the phrase "separation of church and state," he nevertheless voted in favor of the law that allowed parents to use reimbursements of money to bus their children to Catholic schools. If Justice Black agreed with liberal secularlists on the matter of separation of church and state, his ruling in Everson v. Board of Education was a funny way of showing it.
For even more historical descprition on the matter, please read Justice Rehnquist's dissenting opinion for Wallace v. Jaffree (1985). Riveting stuff, let me assure you.
Although it seems clear to me what was meant by the Establishment Clause, many still are not getting it. Rather than leave a legacy of clarity on the issue, all Justice Black did was befuddle it by leaving the Supreme Court, as well as most Americans, in a state of ambiguity. As we shall see, this has lead to inconsistent Supreme Court rulings, which I will outline later, especially in the case of the Ten Commandments being publicly displayed. The fact that anti-religious secularists have obscured the issue with the Everson case makes the issue all the more confusing. However, I hope that these next few days, we can see past much of the confusion.