If your shins are PAINful, rest and ice (to take down the inflamation) are what you want to do, but once they are not PAINful anymore, there is a lot more that you can do.
Shin splints are a often a posture problem, and there is a lot that you can do to prevent the occurance of shin splints and as therapy once you have them.
The posture problem in shin splits is an imbalance between the strength and flexibility in the muscles of your lower leg. The gastrocnemius is the big muscle on the top of your calves, and the soleus is another muscle on the back of your calves. The soleus runs under the gastroc and all the way down your leg to your heel.
The muscle on the front of the lower leg is named tibialis anterior, but I call it the shin muscle.
The gastroc is a large and powerful muscle compared to the shin muscle. In addition, the soleus is often very, very tight. The large and powerful gastroc and the tight soleus are pulling on the opposing muscle group, the shin muscles. The shin muscle is over powered, and pulled back so that it cannot support the bone.
The key to preventing shin splints is to have a strong shin muscle that will support the underlying structure, and to have flexible muscles in the back of your leg.
So you have to stretch and strengthen. Stretch the gastroc and soleus with stride stretches and other calf stretches. To improve flexibility, you should hold each stretch for 30 seconds (really boring, I know), and repeat each stretch 3x. To do both legs with just one stretch will take 3 minutes and it will seem like an eternity of stretching.
If you're interested in strengthening the tibialis anterior you need to resist the dorsiflexion (up or flexing) phase.
You can do this in several different ways. One is to place the heel of one of your feet on the top of the other. The bottom foot will be the working foot. Dorsiflex the bottom foot, using the top foot's heel to supply resistance to the movement in the up direction.
Another method is to place a weight plate on the toes and to lift the plate up by flexing your feet. This often works better with two feet, as you can deal with a larger weight more easily.
Or you can sit with your legs not touching the floor. Take a backpack and hang it around your foot. Lift your foot back towards your shin. As you get stronger, you can add books to the backpack (or bag). Be cautious at first. The shin muscle is a small muscle.