The Caldon Canal is named after the village of Caldon (or Cauldon) but doesn't go within three miles of it. That's because Caldon and, more importantly, the limestone quarries at Caldon Low are high up in the Staffordshire Moorlands, making access by canal alone impractical. For this reason, the Caldon "Canal" was always intended to be a canal plus a tramroad, authorised together by the same act of parliament.

Bridge over Shirley Brook

The first tramroad, completed in 1778, used wooden rails topped with iron which were fixed to wooden sleepers. It ran from the quarries to Froghall Old Wharf by a route which was, in places, steep and uneven. Some sections seem to have been laid on the shallowest of embankments, which are hard to identify on the ground today. The section between Harston Wood and Shirley Hollow is probably the easiest to spot, showing up as a series of embankments and cuttings on the National Library of Scotland's LIDAR map.
This was a railway in the modern sense, in that it used flanged wheels on a smooth rail. In operation, however, it was rather primitive, like a single-track road with passing places. The wagons were pulled along the line singly by horses and when another was met coming the other way, they looked for a passing loop, presumably with loaded wagons heading downward taking priority. The steepness was its biggest downfall, with some sections being almost impassable in winter. The brittle cast-iron rails were also a problem; each one had two holes in it for fixing to the wood beneath and a triangular tongue at one end which fitted into a notch in the following rail. Despite being wider around the holes, the rails would frequently snap at these points and the tongues were liable to break off.

Embankment on the 1785 Line near Cotton

The second tramroad was a not-entirely-successful attempt to address the shortcomings of the first. Firstly and most simply, it was a bit shorter. The canal was extended to a new terminus at Froghall New Wharf, which cut the distance to the quarries by about 500 yards. Secondly, a more thoroughly engineered route with a more even gradient was cut out of the valley side through Harston Wood and out onto Whiston Common. From there on to the quarries, more substantial embankments, much easier to spot in the landscape today, helped to drain and even out the new route. The railway itself, however, employed the same technology and primitive operating practices as its predecessor and, despite the improvements, was still difficult in bad weather. Better technology was needed.

Froghall Great Plane

The third tramroad, designed by the great Scottish engineer, John Rennie, and opened in 1804, was a major change in approach. The new route was divided into heavily-engineered inclines and flat sections. The flat sections were horse-drawn, as before, but with two tracks; one for up and one for down and with wagons martialled into trains, rather than hauled individually. The inclines were "self-acting", which is to say they were powered by gravity. Wagons descending the incline loaded with limestone were connected to empties at the bottom via chains and pulley wheels so that the heavier loaded wagons would pull the empties up. In operation, some of these "empties" were loaded with coal for, amongst others, the copper smelter at Whiston. This was done at least partly to avoid road tolls, causing the local turnpike trust to complain that "revenue was cut by carriage of Coals in the Reelway".
The line itself was a plateway, in which, in contrast to a railway, a smooth wheel runs on a flanged rail or "plate". The plates were mounted on stone sets, rather than sleepers, to allow easy passage for horses in between. The plates had a notch at each end. An iron spike, fitting the notch, was driven into a wooden plug, itself driven into a hole in the stone, securing the plates in position.
John Farey gives a contemporary account of the plateway in his "General View of the Agriculture of Derbyshire" which has been digitised by Google. The Wikipedia entry for the Little Eaton Gangway includes an early 20th century picture of a plateway in action. The Caldon Low plateway seems to have used flat-flanged plates, rather than the curved flange used at Little Eaton.
Although it was a huge improvement on its predecessors, the plateway had its problems. In particular, the cast-iron plates were brittle and liable to snap under heavy loads. Over time, the stone sleepers also became deeply worn (as can be seen in the example below) and, by the 1840's, it was time for a replacement.

Trubshaw's Tunnel

The fourth tramroad, designed by local engineer James Trubshaw, was the most heavily engineered of them all, consisting of a series of self-acting inclines running all the way from the quarries to Froghall Wharf. The horse-drawn flat sections of Rennie's plateway were dispensed with. Where necessary, substantial embankments and cuttings were constructed to keep the incline more-or-less constant and the final section, leading to the quarries, included a tunnel.
The technology used this time was that of a modern-style railway, with flanged wheels running on smooth rails. The top section of each incline used a three-rail layout, in which the centre rail was shared by the up and down lines. Half-way down the incline, the centre rail divided into a conventional double track layout, to form a passing loop. Below the passing loop, the line was single-track, accessed by a point which was set automatically by the descending wagons. Trains of climbing and descending wagons were linked by cables which ran on a series of rollers and guides along the centre of the tracks. At the top of each incline the cables ran into a winding house, where they were wound opposite ways around a brake drum. A train of wagons, loaded with limestone, was let down on one cable which would unwind from the drum. Meanwhile the other cable would be winding on to the drum and pulling a train of empty or part-loaded wagons upwards. Ascending trains would carry especially coal but also passengers on market days and goods for a shop at Hoften's Cross, which had its own siding. The rate of travel would be controlled by a braking mechanism in the winding house, as well as brakes on the wagons.
A similar layout was used on the Denniston Incline, on the South Island of New Zealand until 1967. The Caldon Low version, however, closed in 1920 and limestone to be carried by canal was, instead, loaded from standard-gauge wagons at a new basin near Endon. Deliveries to the limekilns at Froghall continued by road late into the 1930s.

Lower Froghall Plane Today

The short inclined plane leading into Froghall Wharf was used by both the third and fourth lines. The track layout was different but worked on the same principles. A single track at the top split into a double track passing place, controlled by a point, rather than the three-rail system and wagons were let down singly, rather than in trains. The incline was relatively shallow by the standards of the 1804 line but was steep by the standards of the 1847 replacement. This proved awkward in operation but proposals to modify it were never carried out. All that remains today are the foundations for the drum.