For officers, advanced schooling can be obtained through application to the Army's Advanced Civil Schooling Program. If interested, you apply typically as a O-3. For the application, the Arm will look at your GRE score, your college GPA, and your OERs. What matters most in that quotient is your performance while in the Army. If you are a hard-charger and it shows in your OERs, then it helps. It's possible to "out soldier" your GPA. However, there really aren't that many slots for ACS in the Army.
The other way that people can get their masters paid for by the Army is through occupational specialties or their functional areas. Bottom line: if your job requires more schooling, the Army is likely to pay for it. Officers get a chance to select their functional areas typically as senior O-3s, or junior O-4s. However, give the high turnover rate among company grad officers and a high op tempo, it's looking like selecting one's functional area is going to occur earlier.
Here is a list of FAs:
http://usmilitary.about.com/od/army/l/blofficermos.htmWhat an FA is a potential specialty that one can and may serve in if they choose to stay in the Army. The reason for them is that there are fewer and fewer jobs as you get higher in rank. There is a need for specialties and staffs. Not everyone gets to stay on the operational side of things. Depending on the FA you get, you may need more schooling. For example, Foreign Area Officers require advanced schooling in a language, often times at a normal civilian school in addition to DLI. Personnel with an Operations Research FA may usually need school as well.
Beyond these opportunities, there is always the possibility of applying for and getting a med school or law school slot. Some Captain's Career Courses offer the opportunity to get a masters, such as the engineer course. You could apply for a slot as a West Point professor. You could apply to go to West Point as a TAC (and get a masters in counseling). You can pay your own way too, if you so choose. The potential downside for some though in getting the Army to pay for grad school is that you owe 3 years for every year of grad school. As the opportunity to grad school is usually between year 8 and year 11 after. So, say you go at the 8 year mark, do two years of grad school, and return to the force. That means you're locked in till the 16 year mark, at which case you might as well stick around till year 20. It's all a matter of what you want to do in life.
With regards to promotion, in the end it all comes down to performance. If you do well, you'll get promoted. If you do well, you'll get schools. If you do well, the Army will offer incentives, like grad school. Do poorly, and it will take you longer to get promoted and you won't get as many opportunities.
http://usmilitary.about.com/od/promotions/l/blofficerprom.htm