OK -- I can't see a coin counter, so we'll jsut look at the mechs. Beneath each of the mechs, there should be a microswitch with a wire attached. When the coin is dropped in, it should fall through and move the wire, momentarily activating the switch.
On each switch, there are probably three prongs -- one for ground (COM), one for normally open (NO) and one for normally closed (NC). Ignore NC.
I can't see any wires in the pictures -- how many are there and what colours are they (although colours can be deceiving, it is somewhere to start) ?
Cheers.