The best advice I've heard is to do "toe taps" whenever you're not running. Just tap your feet up and down. This strengthens the muscles in your shins, and is reportedly very effective in preventing shin splints. It's an easy exercise to do at your desk, if you have a desk job.
There's also a good thread here at:
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Check that out, too.
Good luck and welcome to Endurance Online. I'm a pretty new runner, too, and have been documenting my progress in the "Beginner Chronicles" thread. Come on over and contribute a post or two!