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!

It's your presence. You should also present yourself as a Type-A personality, even if you're not in your personal life. When you show confidence, you'll speak confidence and it builds from there.

Preparatory command: I act like I am speaking/yelling at someone that is 100m out.
Command of execution: taking a punch to the gut from Tyson.

Sing. In the shower. In your car. Sing big. As if you were singing to a live audience with no microphone. Some say you have to tear your vocal chords apart and rebuild them. That could lead to infections.
Anytime you have a chance sing your ass off. You will be amazed at how fast you will build it up.

When I was a Field Training Officer in a jail I had a trainee that was having trouble projecting his voice to give instructions/information to a housing unit. One day after work I took him into one of our classrooms and had him read something to me out of our policy manual. I sat at the back of the classroom so that he would have to project his voice loud enough for me to be able to hear him clearly. The training worked and he never again had a problem being heard in a housing unit when he wasn't using the intercom.

Step 1- Call Cadence
Step 2- speak as if you are calling cadence

Other than inflection and use your diaphragm there isn’t much too say, what do you want it to sound like? I try to channel my drill sergeant from when I was in osut. “H’ELFT, FAHY. H’ROIHT, FAHY. PITOON, AH-TENSHOON.” Don’t overthink it.

Confidence in what you're saying is key. And we'd all heard multiple people do it before, thus mimicking is part of it as well.