How can God be a person?
Even though God is widely recognized as the greatest person, His form and personality are not widely known about. Even many theists think that, in the ultimate issue, God is formless. Pictures of Lord Krishna playing a flute are commonly dismissed as quaint, mythological representations of the inconceivable, faceless "Divine."
However, there is evidence suggesting that the Supreme Person is not abstract at all. In the Vedas—the oldest and most comprehensive of all world scriptures—one can discover that the Absolute Truth has both impersonal and personal aspects. His eternal, blissful, all-knowing, and all-attractive personality tends to remain hidden behind His all-pervasive majesty and overwhelming greatness.
Since everything in our experience has form and qualities, it makes sense that the source of all sources should also, to an infinite degree. As drops of ocean water have the ocean's qualities in minute degree, our forms and personalities are infinitesimal samples of the infinite Supreme Person.
Vedic writings describe in detail the unlimited names, activities, opulences, and associates of the Supreme Person. Krishna ("all-attractive") is how He's referred to by those who are interested more to His supreme, transcendental personality than to His greatness and opulences.