I never had one, though there used to be someone in the club who used one.
Purely looking at the pictures on the
ebay link, there was a pulley that attached to the hub via zip ties or whatever on the spokes, which drove a pulley on the side of the cyclometer via an O-ring. It looks like the pulley on the cyclometer has two grooves - presumably one would be for 26" wheels and the other for 27"/700c. The cyclometer pulley will drive the counters via bog standard gear cogs.
The cyclometer itself mounted at the dropout. It looks like it was intended to fit between the dropout and the wheel locknut, but I dare say it could also be put on a mudguard bolt.