1. Separation of Church and State is a phrase from a letter that Thomas Jefferson wrote. It's not in the Constitution at all. I should have known this; I just read the Constitution recently, but I hadn't picked up on it and I'm glad that the article's author spelled it out.
2. The First Amendment, like so much of the Constitution, is about balance. Here's the text of the amendment:
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 to assemble, and to petition the Government for a redress of grievances.
They call the first part, "Congress shall make no law respecting an establishment of religion" the establishment clause, and the second part, "or prohibiting the free exercise thereof;" the free exercise clause. They're supposed to balance and complement each other. Congress doesn't get to choose our religion. They don't even get to pick a favorite religion and give them special status. That's the establishment clause. Congress also doesn't get to make it difficult for us to practice our religion. Say, by telling us when and where to pray. Or not to pray, in the case of prayer in school. (That's also a violation of freedom of speech.)
3. There was a bunch of other interesting stuff too: a Supreme Court Justice that was also a member of the KKK, and the founder of the ACLU was a member of the Communist Party of America. Oh, and also what Jefferson was really talking about when he wrote about the separation of church and state. He certainly wasn't saying that churches should be barred from the political process! I highly recommend the article!