And the whole earth was of one language, and of one speech.
Genesis 11:1 King James Version
How did we even get one language let alone the thousands that exist today?
An evolutionary answer might start with a cauldron of silent pond scum, but don’t ask where that pond scum came from. Stir the pot with the magic wand of a gazillion years of random motion until you get some noisy critters. Then keep stirring till the croaks, chirps and growling turn into men and women using language. How this happened, how this even could happen, is the hand-waving that seasons the stew.
What we learn from the Bible is something more reasonable in spite of it being more supernatural. Originally there was only one God-given language, but after God confounded communication at Babel because of disobedience there appeared many others. These were highly complex languages. They simplified over a few thousand years into what we have today.
The following commentary by E. Dane Rogers from the Tacoma Grace Bible Church on Genesis 11 goes into this biblical approach in more detail.
Therefore is the name of it called Babel; because the Lord did there confound the language of all the earth: and from thence did the Lord scatter them abroad upon the face of all the earth.
Genesis 11:9 (KJV)
Poetry, Short Prose and Walking 