How is it that we've had previous births?
The soul is what takes birth again and again.
The Bhagavad-gita's Second Chapter explains that the soul takes on new bodies as one puts on new clothes and then removes them when they become old and useless. The body is temporary. The soul is eternal. The soul takes up residence in a body, due to past karma and according to the will of the Lord. And, although the soul remains "bound" to the body for that lifetime, when the body ages and/or becomes useless, then the soul takes on another body, unless that soul has achieved perfect harmony with the Supreme Lord, at which time the soul returns to the spiritual world and doesn't have to take birth again.