You have to cut the plug, if it has one, off the end of the 'Wall-wart' wires, and the spade connectors off the end of the red wires. Then splice the red wires to the 'wall-wart' wires. You can do this with wire-nus, or by soldering them together. If you solder them together, cover the splices with heat-shrink tubing. Or you can look for a 'wall-wart' that has screw terminals, and connect the red wire space terminals directly. Something like this:

The 'wall-wart' should be between 14-18V and rated at list 1amp (1,000ma). It doesn't matter if it's AC or DC. I get the best performance with 16V.
You asked this same question in the HO forum earlier. It's generally not considered polite to ask the same question in muliple forums.
Len