The most important requirement is that you need a .mil email address, which is proof of being in the US military. Secondly it is necessary to be in the US and have a US phone to sign up for Google Voice. Request an invite at the special military page and Google promises to send you a Google voice invite in 1-2 days. For rest of us, there is the usual Google invite request page.
Google Voice gives you a unique single phone number for all your phones, voicemail becomes as easy as email, and many calling features are free. This video will give you a better idea of how useful your Google number is.
I hope you grabbed your free Google number business cards.