Shin splints are usually a condition of overtraining, but they can also be attributed to wearing the wrong shoes. The simple idea of what happens is that shin splints are the result of the muscles being too overworked to properly support the impact of your feet hitting the ground, and they end up becoming oversensitive, or possibly tear. Training in shoes that aren't designed for long-distance runs will definitely cause some damage.
Treat shin splints by resting. Don't run at all, at least until you can go day-to-day without any pain. When you get back to training, either run shorter distances with longer rest intervals, or use an alternate training method such as bicycling or swimming for a few months.