Allow me to preface my remarks by saying that I am not a lawyer, I am not a college graduate who is studied any of the law. And this is just a plain text reading and understanding of it, prior to any judicial presidents.
The First Amendment to the United States Constitution-
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.
First, to understand the need for this amendment ,you would do well to remember that at the time of the framing of this document, the United States had just broken away from England. At that time the church had unspoken control over the state. England basically had a state instituted religion, the Church of England .if the state should make a law that the church did not like, the state would have to throw their law out.
In looking over this amendment you will notice that it specifically states Congress shall make no law respecting religion for or against it .it does not say that it does not want religion in government, or for the people not to practice it. In this way the framers left open the choice of the people to either practice or not practice a religion.
The first part shows that Congress cannot say you will practice a religion, and follow these rules of that ,or belong to a specific sect of religion .
The second part says that Congress cannot say you can not practice a religion .
In all this it recognizes that Congress is the lawmaker and says Congress cannot make any laws for or against it therefore leaving the individual practice up to the people .
This also says, that because there cannot be any laws for or against ,that if a particular department of the government wishes to insert prayer they are welcome to as it is not prohibited . As a matter of point Congress since the inception has always started off with a prayer .this is important to signify that the framers were okay with religion and government .or if they did not want religion and government as so many group’s say ,they would not start each session off with prayer.
So to all the organizations against prayer, your thoughts on the Constitution prohibiting it in government are misled. As the framers, some religious some not, deemed it important to leave the choice of the expression of religion to the people that either wish or not to practice that religion, and not too exclude it from the possibility that you may wish to exercise the right of religion .