In Italy's case, the normative framework varied from city to city (as did the side of the road one had to drive in, at least until 1929). In 1898 the comune of Milan was the first in the country to introduce a specific "driving concession" which was granted only after a thorough medical and psychological examination by a selected municipal committee - but apart from this, well, you just had to learn how to drive the damn contraption by yourself!

A few years later, in 1901, Royal Decree n. 416 established the first resemblance of a nation-wide licencing scheme: in order to get their own, prospective drivers had to make a formal request to the local prefect and then they had to pass a specific exam aimed at demonstrating their familiarity with the machine... they just bought. The exam in question was administered by officials from the Kingdom's public works office (Genio Civile) and once passed, the candidate got the licence proper - the one our driver had requested at the beginning of his/her bureaucratic adventure - as well as a small booklet bearing his/her signature and a photo. Eventual fines were annotated there.

Licence plates and speed limits weren't introduced until some time after (Regio Decreto 8 gennaio 1905, n. 24).

Were there any driving instructors at the time?

Nope. Driving schools and instructors won't appear before a few decades, with the country's mass motorisation.