Government shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof. Pretty simple. An "established" religion is a state church. A law, for example, that said that the Baptist faith was the official faith of the United States.
That's all there is too it. Church schools can get lunch money, money to pay for school buses, and a tax exemption. But there can be no established religion.
Today the Supreme Court said a Missouri school can have state money to improve a church school playground. Nothing in the constitution that prohibits this.