Pete, that is a mechanical gauge, not too different than the one I have in my TR3A (except for the color scheme). The probe remains permanently attached to the gauge; inside that spring-looking thing is actually a very fine bore tube (commonly called capillary tubing because of it's small inside diameter). If you kink or crack the tube, the gauge will stop working.
Should be an easy installation, but check your thermostat housing (or wherever the probe goes) to be sure it has the surface that the lip of the probe butts up against. The nut has straight (not tapered/pipe) threads and bears against the outer surface of the lip, so the inner surface forms the seal against the housing. If your housing doesn't have that surface or it's not in good condition, you'll need an adapter to go between the nut & housing.
You'll probably also want to find the bulb holder that fits into that open hole. Tap the wire into the red wire behind the dash, so the bulb comes on with the dash lights.
At the very least disconnect the battery, preferably remove it entirely. The capillary tube will flop all over as you thread it through the car (starting from the cockpit obviously, and ending at the thermostat housing). You wouldn't want it to touch a battery terminal (particularly since the ether inside the bulb/tube is flammable).