Check your footwear to begin with. There are actually a few shops in CT that will do some video monitoring of you running and prescribe sneakers based upon your foot mechanics. New Balance in South Windsor and Fleet Feet Sports in West Hartford are two that come to mind.
Next, strengthen your tibialis anterior. Shin splints are actually inflammation and damage to the interosseus membrane (a layer of connective tissue between the tibia and fibula that several dorsi flexion muscles connect to). Sometimes when the TA isn't strong enough, other muscles compensate, and their extra force production leads to what you feel as shin splits.
Finally, and perhaps most important, stretch your calves. Do both the straight knee (for the gastrocnemius) and bent knee (for the soleus) stretches. Some good manual massage work will help as well.
And, you can always ice your shins, but that is only a temporary fix to reduce inflammation and pain.