If you have a lot of early copies of some documents, and those copies match up with each other, you can know with a lot of certainty what the original documents said.
Put it this way: We have less than 700 copies of Homer's Iliad and they were from an era about 400 years after he first wrote this famous work. This is considered good in historical literature, but the New Testament is far better.
The New Testament of the Bible has over 5000 manuscripts that were from less than 100 years of the originals.
Check out the table from carm.org for more info on this.
This puts to an end any foolish notion that the manuscripts of the New Testament were corrupted (as Islam claims). To ensure this corruption you would have had to gather up all of these 5000+ documents and change them. If you missed just one it would be obvious what had happened.