According to the Mayo Clinic:
The term “shin splints” refers to pain along the shinbone (tibia) — the large bone in the front of your lower leg. The pain is caused by an overload on the shinbone and the connective tissues that attach your muscles to the bone.

image borrowed from the Mayo Clinic
The most common causes of shin splints are:
Tightness or weakness of the calf muscles and muscles in the tibia area
Inadequate footwear / inadequate arch support
Overpronation in the feet
Oversupination in the feet
Repeated running on hard surfaces such as concrete
Uneven surfaces
Beginning training after a long period of layoff
Inadequate footwear and re-introduction of training as well as decreases in strength in supporting muscles are the main reasons why shin splints tend to be more common during pre-season and early season training.
So how are shin splints treated? Much like other types of soreness, remedies include:
Utilizing the PRICE method
Taking aspirin or another such over-the-counter anti-inflammatory
Using muscle rub such as Tiger Balm
or Icy Hot
Massaging the sore area
In addition to those, there other possible remedies which might apply depending on the cause of the shin splints. They are:
Wear different footwear – including possibly corrective footwear for overpronation or oversuplination
Utilize arch supports or cushioned inserts (I’ve linked to the ones I personally wear) in your shoes
Employ shin splint taping
Train on a softer surface
Reduce activity for in the short-term, and gradually increase