Col (Dr) Don Snider (USA, Ret) has a well thought-out article on the Christian military witness at Journal of Faith and War.  He notes the complexity of the issue with a single opening phrase:

There are no formulas, Christ only said: “Render unto Caesar what is Caesar’s, and unto God what is God’s.”

His points fall under the following categories:

Mastering the Context
“…you are not to compartment your life and its varied roles (supposing that you actually could do so psychologically which is, of course, quite debatable). You may not choose to be a Soldier leader in some settings and a Christian in others.” 

“You are, in addition, free to witness appropriately to your faith, even as you fulfill your military responsibilities. The great freedom to religious expression is, after all, one of the reasons most of us have accepted an oath to serve and defend the Republic and its way of life…It is one of your tasks to be well informed as to what “appropriate” means in the context I just used it.”

Under your Military Calling
“The leadership imperatives have not changed: military competence and moral character manifested in presence, decisions, and actions…the leader’s daily practice must consistently be one of “professional excellence,” clearly reflecting the leadership imperatives of military competence and moral character…”

Under Your Christian Calling
“…we are called to both “hear and do,” and the doing requires an ongoing witness to Jesus Christ and his Gospel. As mentioned earlier, these passages do not allow closet Christians, those who hide their faith…”

Synthesis: An Authentic Witness under Your Dual Callings
“I recommend that you choose to be a positive witness first and foremost by your professional excellence, by demonstrating both your military competence and your moral character.”

The Individual Practices of the Soldier Christian that Produce an Authentic Witness
Die daily to self
Be Steeped in God’s Truth
Remain empowered by the Holy Spirit
Live a life of simplicity

Col Snider’s article comprises an excellent overview of Christian living in the military.  At 3,000 words the commentary is somewhat lengthy, but it is absolutely well worth the read.