I always smile when I see the question of "how do we know" come up because the Bible itself, and its survival, is a miracle we take for granted.
There are 39 ancient texts that confirm or refer to events, people or various other things known in the Old Testament which were not the texts the bible itself comes from. No other historically accepted document has such supporting evidence.
No other book is written by so many different people, from different walks of life, different regions of the world, over thousands of years - and yet.. supports and confirms what is written. In one place you have a prophecy, in another you have historical recording of the fulfillment of that same prophecy.
No recorded document in history has had so many powerful enemies try to destroy it, and yet survived. Its been burned, banned, the writers or printers or distibutors put to death, and yet - IT survives.
It doesn't change. Sure, new translations come out, we obtain better understanding of what is written, but the basic message NEVER changes. Always God is the Creator, always the Alpha and Omega.
The book of Mormon changes when the prophet of their church changes. The Koran supports the old testament to a point, then splits off, and changes.
How do we know the bible is really His word? He protects it. We can't even destroy His word when we try.