There are a couple of common causes of blisters while running, but the most common by far is poorly fitting shoes. Shoes that are too loose allow for rubbing and friction, and this can lead to blisters. At the same time, shoes that are too tight will lead to pressure points, for example over the big toe or at the back of the heel, and these also will lead to blisters! Therefore, the first thing I would do if I were you is go to a good athletic shoe store to make sure that your shoes fit properly and are designed adequately to support your foot time. It can also be helpful to ask for advice about the type of athletic socks to use, as wet socks also contribute to friction and skin breakdown. Switching to a better, wicking form of sock that keeps the feet dry can help a lot.
As you continue to run, your feet will get tougher and the number of times you experience blisters will decrease. In the meantime, make sure to cover any areas of blister or soreness with moleskin when you go out for a run. Talk to your primary care doctor
if there are any spots that look infected or do not seem to be healing well.