USAA banking is available to everyone. Some nicer services (deposit by phone, insurance) are for service members only.
For what it's worth, my brother (Air Force) sold me on USAA after he signed up with them. I worked at Wells Fargo at the time, so I had the best accounts. I'm happy I made the switch. Also, their web interface and iOS apps are excellent. By far the best I've seen.
Like others have said, there is an app. Prior to the app (and still available), you would scan both sides of the check and email the images.
They also have a deal with UPS that allows you to go to a UPS store where they swipe your ATM card, scan the check and process the deposit. It's free. I believe the UPS method is the only one available to USAA bank customers that are not eligible for the insurance products. It's not too bad. There are a lot of UPS stores and their hours are at least as good as most banks.
It's amazing. I started a new job and their paycheck provider screwed up, so I wound up with paper checks. I couldn't afford the delay in mailing them to USAA, so I tried the app deposit method. Take a pic of front, take one of back (after writing a few lines 'deposit only' yada, yada), and it was deposited instantly.
You enter the details of the check, how much it is for and the like. You take a picture of the front and back of the check. That is it. They must do some sort of OCR on the image you upload because it usually takes me more than one try before it will accept most of the checks I have tried.
For what it's worth, my brother (Air Force) sold me on USAA after he signed up with them. I worked at Wells Fargo at the time, so I had the best accounts. I'm happy I made the switch. Also, their web interface and iOS apps are excellent. By far the best I've seen.