As gruntpain stated, there are no official programs for obtaining a driver's license. That said, most leaders support and encourage getting your license and will help in any way they can. I have personally taken two Soldiers to DMV and even let one use my car to take the driving test.
A military DL is based on a civilian one, and if you're stationed overseas (other than OEF/OIF), an international DL will be needed if you want to drive anywhere.
Of course, if you want to bike, hike, fly or take a train, that's different. All you need is a credit card, cash or a bike.