How would a business that was outsourcing CAD work get the .dwg files to the contractor? and vice versa?

There are several ways to do this.
 
The most effective way is using the eTransmit function in AutoCAD - it makes sure that no external reference, font or shape file will be missing.
 
If you need versioning, automatic notification of updates, check-in/check-out, logging and security, you can consider iPROJECT - see www.xanadu.cz/en/iproject.asp