1. To modify an object to suit another purpose from it's original, often very dangerously, however.
2. To build a tool out of scrapped materials, commonly used in the repair of objects, or to substitute a tool.
As used in a zombie invasion;
Tom: I finally used redneck engineering on a weapon.
(Lifts up a metal pole with a bowie knife attached using massive amounts of duct tape and welding.)
Bill: That'll be useful, man. Good work there!
As used incorrectly:
LOL I REDNEK INGINERED A $10 DOLLAR BOARD GAME WITH MY IPAD! YOU GUIZ WANT TO PLAY WITH YOUR IPOD TOUCHS?