Wear correct running shoes, don't over do road running and check you have a decent running gait and you aren't pounding the ground necessarily. Keep your calf muscles nice and supple and well stretched as well. Takes the pressure off the shin bone.
Do an Arrse search, there's a massive thread on them on here somewhere, sorry, I can't be arrsed to find the link. I find taking brufen about half an hour before a run, and icing my shins straight after works a treat. Also, when you're in bed before you go to sleep, lie on your back and pull your toes as far as you can towards your knees (using your shin muscles, nothing else!). Don't pound pavement if you don't have to, the Army won't have you running on tarmac very often, so train for what you'll be doing! Find a field or somewhere with soft(ish) ground and run on there.