You don't.
Since you've already got all those stripped wires you'll just want to build a little VGA->Arcade Monitor harness.
There are several threads active right now discussing this. In a nut shell you'll connect pins 1(R), 2(G), 3(B), 14(VSync), 13(Hsync) to their respective pins on your monitor. The Red green and blue wires from your first picture are probably correctly color coded.

You'll want to run the program Soft15Khz to enable the low resolution modes that an arcade monitor requires. There's a thread on that too.
Probably want to start poking around the Wiki and reading up on various video topics. It's not as straight forward most of the time as it seems.