How do Drill Sergeants, Drill Instructors, and NCOs develop a command voice?

While many here will give you the detailed by the numbers methodology they used I just mimicked the voices of Senior NCO's I served under and added my own brand of vocalizing to it. The big thing is as you have said is not to yell but to uses your diaphragm to make your command voice louder without killing your throat or sounding like a frog. Some would tell you to practice in front of a mirror but I learned my method by practicing giving commands as a (PFC)Team leader and (SP4)Squad leader. By the time I made PSG I had it down pat and rarely hurt my throat. Singing cadence also helped me. The best way to learn this is to do this, when you can give a prepatory command that can be heard by a formation and nobody laughs you have it. The simple fact is PRACTICE make perfect. Unless you sound like a chicken in heat the troops will hear you, understand you and execute your commands. These days young folks have many sources to perfect their command voice both online and in movies as well as peer coaching. Good luck.

P.S. I can do a fairly convincing MARINE impersonation for my Marine turned Army troops and if you can trick them with that mumbling drawl you can do anything :)

Cadet SGT Ali Burianek - Yours is a great question and I'm glad I read the reply by 1SG Hicks before answering, for he has given you the best advice you will get today. Listen, Emulate, Practice (Loudness and Projection)
By way of example, 1SG Homer Howard of Charlie company (I was a slick-sleeve private in Bravo) was a Korean war veteran whose voice sounded like a thunder-clap. In fact, it startled me the first time I heard him bark out "Charlie Cump-ney, Fall In" and I remember thinking that was a bit over the top. But in time I grew to appreciate the authority that voice commanded and began to copy it.
His voice is my command voice to this day. Practice time can be difficult to find without annoying other people so I would practice while driving and if anyone heard me over the din of traffic, I neither knew nor cared - It fulfilled the purpose. One more thing. Remember to clear your throat a bit before giving a command until you are proficient in that practice, lest you risk sounding like a school-girl at recess. Good Luck!

Cadet SGT Ali Burianek PRACTICE! Practice matching yourself about.

Always do a physical recon of the route to your intended destination before you attempt to march troops there. Marching Soldiers into a dead end street was very embarrassing!