The carding I know of has steel needles attached to wooden blocks that are used to clean wool by separating it up with the teeth. Wikipedia didn't tell me when this first began though, and if there were alternatives before then...
What would carding have been like in the 15th, 16th, 17th and 18th centuries?
Needles in wooden blocks for carding go back at least as far as early Anglo-Saxon England. They found a set in a grave in the 5th-7th century cemetery at Lechlade, England. They look almost identical to the ones that are still used by crafters today; it's one of those technologies, like hammers and chisels, that haven't changed much in milennia because they work so well.
The ancient Greeks used pottery combs, plates of ceramic with the surface brought up in spikes when being shaped. Naturally, they wore out, and wound up in midden heaps or used for ostracons.
As I have photos in books of Greek peasant women spinning wool in the ancient manner with a hand spindle, there's no telling how long the pottery combs lasted.