Tracking (homing, more accurately) using a DME alone was a required part of an Oz IR with a 'DME Descent' endorsement (ie 'approval'. Australia requires a endorsement for each tracking aid you wish to use as part of your instrument rating). A DME Descent is an now obsolete (except, I think, in PNG where OzEx keeps some around for the fun of it...
) type of circling instrument approach that completes a 'DME Homing & Descent' procedure.
It typically was used to meet alternate approach procedure requirements in more remote areas where it would be prohibitive or impossible to carry enough fuel to fly to another airstrip with a useable instrument approach. Distances can be rather large between approaches in Oz... Lots of places would have a single azimuth aid (NDB mostly, occasionally VOR) with or without a DME. Those with a DME would usually have a DME Descent available. OCTA & no radar available either.
Generally the expectation was that it was a backup, to be used if all the azimuth aids fail. The scenario then involves orienting to the DME, homing to it & completing the approach, all using DME alone.
Orienting was usually quite easy. You probably were already tracking to the station so approximate direction was already known. It could also be an off-track diversion in which case an initial orientation would need to be done. I liked to do a rate one turn & watch the rate of closure & distance. Note the distance when ROC is zero, then note the distance when ROC is zero heading in the other direction. Turn 90 deg towards the station.
Homing involved finding the required HDG by assuming a number of 30 deg heading changes in the same sense & noting the ROC (or, for the older DME equipment that didn't have ROC functions, timing over a distance to find ROC). As HDG became more & more towards the station the ROC would increase. When a 30 deg turn eventually resulted in a reduced ROC then HDG was turned 15 deg in the opposite direction. This is 'bracketing'. Periodically you'd have to rebracket. A log of the required HDG & ROC would give enough info to have a reasonable stab at estimating W/V & drift allowance to better track to the aid instead of homing.
The requirement was to arrive within 2 DME of the aid. HINT: Descend to LSALT/MSA some miles prior to the aid. It gives a greater lateral distance to stay within tolerance compared to staying high.
If you couldn't get within 2 nm on first arrival but were within ~ 10DME and saw the distance start to increase a series of turns based on distance would get you within tolerance. If you turned the wrong way then continue the turn into a 270 deg.
The Descent part involved a timed HDG outbound and a procedure turn to head inbound. Can't remember, but it might have always been an 80/260 procedure turn rather than a base turn. Descent would similar to NDB or VOR approaches, either commencing outbound with a limit until inbound or commencing inbound. You had to arrive back within 2 DME after the inbound leg.
If you were smart you'd pay attention to the wind effect at LSALT while still homing inbound & use that information to lay off drift on the Descent's out- & inbound legs. Made getting back into the 2nm circle a bit easier. No fancy turns to compensate as could be done with impunity above LSALT/MSA.
I never had to do one in anger, although often used the DME to meet alternate approach requirements.