How do we practice separation of church and state?

I say we just take a look at what the Framers had to say about the 1st Amendment and the whole discourse on Seperation. It is EASY to avoid the Up/Down, Right/Wrong crap when religion is kept out of the public venue IN TERMS OF GOVERNANCE. Just consider what Madison (an architect of the Bill of Rights and the early amendments) had to say about religion.
“Is the appointment of Chaplains to the two Houses of Congress consistent with the Constitution, and with the pure principle of religious freedom? In strictness the answer on both points must be in the negative. The Constitution of the U. S. forbids everything like an establishment of a national religion.”
And then goes on to say. “The establishment of the chaplainship to Congs is a palpable violation of equal rights, as well as of Constitutional principles:”
He says much the same about military chaplains.
James Madison, Detached Memoranda/ca. 1817W. & M. Q., 3d ser., 3:554--60 1946
http://press-pubs.uchicago.edu/founders/documents/amendI_religions64.html
I am not interested in hearing ANY RELIGIOUS DISCUSSION other than a general condemnation of it.

Keep your beliefs to yourself. Stop proselytizing.

Easy. The government has no say on what happens within the walls of a religious building, and the religions have no say on what happens in the government/the country.

Offensive? Not at all... pretty honest and forthcoming actually... I envision a small group of grey haired people singing 400 year old hymns and nodding off during a "fire and brimstone" sermon about Leviticus and Revelations though. Not the kind of place I'd choose to worship.

As for separation of Church and state...

When Kennedy was elected there was fear that because he was Catholic that the edict of the Pope would find their way into the laws of the United States. I think history has proven that it was not the case.

Integrity and moral character are imperative for the leader of the most powerful nation on the planet. When Jesus was asked what the most important commandment is he responded:

“Love the Lord your God with all your heart, with all your soul, and with all your mind. This is the greatest and most important commandment. The second is like it: Love your neighbor as yourself. All the Law and the Prophets depend on these two commandments” (Matthew 22:37–40)

Awareness of the struggles of our fellow citizens is implied in this edict... and often forgotten, but isn't the mark of a great president the ability to consider what is best for the citizens of the United States and the world?

Heh. There's a few Republican Baptist Churches in the South. At least they're honest about their politics.

Are they violating the seperation between church and state? Probably. Do they care? No. Is the IRS going to yank their 501(c) status? Get real.

Churches that adhere to the church/state rules are the ones you never hear about.

I think the better question is how do you adhere to the doctrine of separation and balance that with "Freedom of Religion?" Every time a politician, who is also an American Citizen guaranteed inalienable rights, says something of a religious nature, the anti-religion crowd throws a terrible-two's tantrum.

As long as Congress is not establishing a state religion there is not a Constitutional problem.

The government should stay out of the people's and the church's business, and let them worship (or not) as they choose.

I don't go to church except for funerals. It never enters my mind

This is an interesting question. I personally would advocate the separation of church and state, but as you said, how do we go about this?

If we have our own beliefs, won't our decisions always be biased toward that? And if we make those biased decisions, won't that always influence our politics? How does one separate their religious/moral obligations from the political decision making process? Although this situation would be ideal for me, I'm not sure it is completely possible.

Interesting question CH (MAJ) William Beaver. Since the church is another name for the bride of Christ and consists of every believer who has does or will exist the church transcends any particular nation or group of nations. The church is greater than the state. As Christ said "render under Caesar [the state] the things that are Caesar's and unto God the things that are God's."
As believers with the light of Christ shining through us we can not separate our faith from our duty to the state. Separation of church and state fits well in deism which Thomas Jefferson practiced; but, we should not be expected to behave differently in matters spiritual from those that are temporal.