OK - I used to run a LOT for school. Each year at the begining of training, I would get shin splints (and look like a robot going to class for weeks). I discovered the following things help "get rid" of them quicker:
1. There is no magic pill that will get rid of them overnight - you need to train shins throughout the day EVERYDAY
2. Do toe lifts as often as you can during the day. These are done while standing (as often as you can ) by planting your heal on the floor and raising your foot up as high as possible (toes toward the sky). You should feel pressure on your shins. Hold the tension for 20 seconds or so, then switch to the other leg. Do 3 or 4 of these as OFTEN AS YOU CAN THROUGHOUT THE DAY. Anytime you are standing around.. do as Nike says "JUST DO IT".
2. Before running/doign whatever it is that causes the shin splints, do this warmup. Lift your whole foot off the floot (suspend it in the air). Rotate your foot around the ankle in one direction about 10~20 times (feel the pull in the rotation). Switch directions for the same amount, then switch feet. Do this during your warmdown as well.
3. Find a shoe that fits YOUR feet well. This is an individual thing. I swear by ASICS (lots of runners do) but some people prefer nike (they KILL my feet, but some people do better with them) or others.
Thats it. Where possible, work the calfs/shins. The only way to get rid of shin splints in the long haul is to strengthen them up. PERSEVERANCE will pay off. I never get them anymore - even on 20 + mile runs

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