Reading the Tenth Chapter ( Dasham Skandha ) of the Bhagavad Purana. This, along with the Vishnu Purana, is the source of all subsequent writings in various Indian languages of Lord Krishna's birth, childhood, youth and manhood e.g. Geet Govindam by Jayadev, poetry of Surdas, Raskhan, Mirabai, Vidyapati, Narottamdas, Ratnakar, the Alvar Tamil saints like Andal ( see Tiruppavai ), etc
The Mahabharata does not mention anything about Lord Krishna's birth, childhood and youth. He is already an adult when he appears first in the Mahabharata. So we have to go to the Bhagavad Purana ( also known simply as Bhagavad ) to know about his earlier life.
The Bhagavad ( not to be confused with the Bhagavad Gita, which is part of the Mahabharata ) is in Sanskrit. The Tenth Chapter, dealing with the birth and early life of Lord Krishna, is the longest chapter, one fourth the entire Bhagavad. It describes the birth of Lord Krishna, the atrocities of his maternal uncle Kansa, the carrying away of Krishna by Nanda across the river Jamuna, the killing of the demons Putana, Trinavarta, Aghasura, Dhenuka etc, the naughtiness and childhood pranks of Krishna e.g. stealing butter, etc, Yashoda's binding him, the chastising of the serpent Kaliya, the swallowing of the forest fire, raas leela with the gopis of Vrindavan, the lifting of Govardhan hill, the return to Mathura and killing of Kansa, the fight with Jarasandh and migration to Dwarka, the kidnapping of Rukmani, the slaying of Jarasandh and liberation of kings, the visit of Sudama, etc.
Surprisingly, there is no mention of the Mahabharata war in the Bhagavad Purana