(2004 Lincoln Navigator) How do I set up these screens in the back?

All that loose wiring suggests that the cabling or the electronics (or both) have been modified or changed, and aren't stock.

In order to get things working, I think you'll have to go to a car audio/video store (where equipment like this is sold and installed) and get them to figure out what components are in the vehicle now, and how those components are connected.