OK Tom, excellent photos. This looks like it will be an easy one, well at least not very complicated.
A common convention (but there is no defined standard) is;
LPT Port Pin 2 X Step
3 X Direction
4 Y Step
5 Y Direction
6 Z Step
7 Z Direction
With pins 18-25 as GND or 0 Volts.
This is the very basic and initial connections required to move the motors but there may be an enable signal (e-stop) to be found also.
If it was me, I would connect the cable to your computers printer port and try configuring Mach with the above pin allocations (2 to 7) as trial and error and see what happens. Once you get axis movement then you need to set the steps per and velocity / acceleration etc. for each axis and get the directions right. (the Mach manual and videos will give you more details of this).
The next step is to find the limit / homing switch, e-stop and spindle control pins (2-9, 1[seldom used], 14, 16 & 17 are all output pins driving the machine functions) (10-13 &15 are all input pins connected to e-stop, limits, safety interlocks etc.) (18-25 are ground)
Good luck with the experiments.
Tweakie.