I previously suffered a horrible case of shin splints. Mine got so bad that after running once a lump appeared on the inside of my shin.
In my opinion the number one thing is to get a good pair of running shoes. Find a store that specializes in running and they will take a look at your arches and be able to find the right pair for you. Cross trainers will not suffice if you suffer from shin splints. They may even want to see the soles of shoes you already own so they can identify whether or not your foot rolls inward or outward when your feet land. Also make sure your shoes are laced/tied tightly to reduce your shoe moving around.
Another common cause is the surface that you run on. Concrete is the worst because your foot has to absorb all of the impact. Grass is probably the best. When I developed shin splints I still had to run and was able to do so if in the grass, if I took a few steps on concrete while running it got agggrevated again.
Do some light stretches before running, just don't overdo it. When you're finished try epsom salt baths,contrast showers,ice packs-whatever you like. One product that I now swear by is veterinary liniment. It may be similar in nature to the different boxing liniments available. Essentially it helps with the pain, and speeds recovery by increasing blood flow to the area. You can find it at most agricultural centers in the horse sections. Just don't rub your eyes until you're sure its all off of your hands.
For the time being, since you've already developed shin splints, cut back on your running. As much as I hated it I rode on an exercise bike to keep my cardio up while my shins healed.
I know how much shin splints suck but give it time and find an alternate method of training until you're healed up. It took me months to actually be pain free from them but I can now run without any issues.