Your dog's feet are like the tires on your vehicle. if they are not cared for you will not get far. Get your dog used to having their feet handled. Picking up the feet, spreading the toes and looking in between. Check toenail length, keeping them clipped back is essential. If your dog has dew claws keep them short as well. It does not matter if the dog is standing or lying down. I find it easier for the first time after a run they are tired and easier to handle.
Create a habit of checking each foot after each run. Looking for pad wear, tears on the pad. Look inside the underside of the foot for splits. Practice putting on booties BEFORE you need them.
Familiarize yourself with the anatomy of the your dogs feet. This will help you understand why these things occur and how to heal injuries and perhaps prevent them.
Keep it fun; you and your dog will be pros in no time.