In Genesis, how did the first language come to be? How did Adam, and then Eve, learn to speak?
By being made in the image of God, God granted man one of his attributes- namely the ability to communicate. As a God in communion and relationship with himself ("let us create man in our image Gen 1.26) the power of speech and language would have been understood to merely be part of that Imago Dei. 

Furthermore, the fact that Adam was given the job of naming the animals indicates that God had given Adam the power of speech. 

The Paley hypothesis, popular in the 1800s suggested that God created creatures fully adult like, so God creating a speaking Adam would have been perfectly natural.