How do I go about marrying a German citizen when I am stationed stateside? How do I get her to the states with me?

Congrats. I’m sure you’ll get some help here but I’d also recommend checking both with personnel and your commands Chaplain.

She can apply for a K-1 Visa (see State Department Web site, https://travel.state.gov/content/travel/en/us-visas/immigrate/family-immigration/nonimmigrant-visa-for-a-fiance-k-1.html). You should also consult with your chain of command so they at least know what you're doing. They may be able to help you. Check with your security officer or NCO to make sure the marriage won't adversely impact your security clearance. Also you could talk with a Chaplain. Once she's legally in the US, you can marry as provided for in the state in which you get married. State web sites normally explain the process. No fancy ceremony is needed. A justice of the peace or similar official can do the marriage in many states. Once you are officially married, then get with your S-1 for assistance getting her recorded in DEERS leading to official dependent ID card. Update all the other personnel and financial stuff like SGLI beneficiary, etc.

I was able to get my wife to the states on a fiancé visa in 2015. Started the process in July and she flew over in December. Married in Feb. The biggest issues I see right now are going to be for her. I live in Germany right now, so most of the agencies she will need to visit are closed or backed up. You can do the process yourself, which is what I did for her green card, but for the K1 I used RapidVisa. They made it easy for me. Especially being busy with the Army and stuff.