The catch is that you already have to be a nurse with a BSN, be a commissioned officer, and have at least three years of critical care experience in the military as well as a strong academic record. CRNA school is 2-3 years depending on the program, so you would owe a service commitment of 4-6 years thereafter.
Your competition to get into the program are other nurses in the military with experience. Like anything competitive, you have to compete. If you're already a nurse with a BSN, your first step is talking with a recruiter. The Army has consolidated recruiting; the USAF and Navy do not. They have different recruiters for officers. If you have a BSN and are otherwise qualified, you can come in on a direct commission as a 2nd lieutenant. Put in your time as a military nurse, get some ICU experience, and put in your package for CRNA school. If you're accepted, you'll be on pay status while you attend school and they'll foot the bill. Then you owe your service commitment. If you drop out of the program or don't complete your service obligation, they will reclaim the money they spent.
It's a program for career military nurses. It's competitive to get into and it comes with a significant obligation afterward. They don't want to spend all that time and money training someone who is just going to get out. They need CRNAs, not graduate students. It's not a jobs program, its purpose is to fulfill a critical need in military health care. They want to make sure those nurses are going to stick around. So they start with nurses who have already been in for a while and they obligate them to further service. If you've already been in for 4-5 years before you're accepted to school, put in another 2-3 years there, and then have to serve another 4-6 after that -- you're already at 10-15 years. Might as well stick it out to retirement at that point if it's only another five years. They want career nurses.
Alternatively, you can enlist, serve your commitment, get out, get your BSN, then use your GI Bill to cover graduate school. That would also technically be the military paying for CRNA school.
If your intent is to find a cheap way to get a degree that pays six-figures, this isn't the program for you.
Former USAF flight medic and training manager