Compared to most other Western populations Americans are very religious. Around 40% visit their place of worship at least once per week.
The majority of the population is Christian, either from denominations also normal among Europeans (Catholic, Lutheran Protestant, Episcopalians=Church of England, Calvinists), but there are also Southern Baptists, Presbyterians, Amish, Mennonites, and a host of local churches of more American invention. There are Mormons (if they are seen as a Christian denomination depends on who you ask,) Jehova's Witnesses, Unitarians, Quakers. There are Jews, Muslims, Hindus, Buddhists, Confucians, Sikhs, Rosicrucians, Zaratustrians, Agnostics, and Atheists - my apologies to those not listed, no disrespect intended.
Religion plays a big role in the public discourse. That said, politics and religion are not common subjects for conversation with your friends over dinner. Because many feel so strongly about their faith (and their political position), it is a hard gap to bridge if your friends believe something totally different. To agree to disagree is unfortunately not so common.
So most of the public discourse takes place in the public media - and before the courts. The number of cases where somebody - atheist of believer - feels that his/her religious freedom has been infringed upon is astounding. Articles in the news with religious content is common and the comment sections in the bloggosphere when religious matters are debated easily outnumber discussions about more secular subjects - even those that have great influence on personal freedoms or discuss Supreme Court decisions.
To understand this aspect of American culture I can strongly recommend reading Jonathan Haidt's "The Rightious Mind - Why Good People are Divided by Politics and Religion" or - also referred in the Theory section of this website - "Changing values, persisting cultures: case studies in value change" edited by Thorleif Pettersson and Yilmaz Esmer. Follow the link and scroll down to page 9 (not ix but 9), "America The Traditional" by Wayne E. Baker. For a comprehensive history of the special American brands of protestants, T.M. Luhrmann's "When God Talks Back" offers up an anthropologic perspective.
Although you may not agree with the positions in these texts, they may give you a little more appreciation for the miracle it really is that so many people from all over the world have succeeded at living mostly peacefully together in the US. In the until fairly recently very homogeneous European countries we are only beginning to face the challenge of uniting peoples from different cultures and with different histories into one nation.