Just use a breakout cable. ( a standard vga cable with the end stripped off)
Locate the RED, GREEN, BLUE, SYNC, GROUND etc on the vga cable and then tie those directly into the monitor according to it's required pinout.
Since most arcade monitors require "composite" sync you would just tie the H and V sync from the vga cable together to the composite sync pin on the monitor.
And the rest are self explanitory, R, G, B, Ground.