Welcome to the forum. It is indeed a great site.
As best I can tell from reading the section pertaining to transfering firearms in MN (Link Removed beginning on page 6, left column, near the bottom) It appears to me that in MN you are able to obtain a "transferee permit" which allows you to purchase handguns or certain assault weapons without filing any paperwork. Additionally, a CCW permit is also a valid substitute for the transferee permit.
If it is a private sale, it looks like all you must do is verify the ID and the permit of the purchaser. I would suggest making a photo copy of both.
I'm not a lawyer, so of course take my advice at your own risk.