Roman taxation overall is a complex question that has varying answers based on location and period. Generally taxation involved poll taxes, land taxes, and customs duties, not income tax per se.

With regard to the gospel passage, tt is probably a reference to the poll tax (a fixed tax per person) introduced into Judea following direct Roman rule from 6AD onwards. Josephus mentions this taxation in relation to revolutionary attempts by someone named Judas. This is found in Josephus Wars 2.117-8, as well as Antiquities 18.4-10.

This makes sense of the gospel contexts, in which the question posed to Jesus seems to be an attempt to draw his opinion on a controversial topic, whether he was sympathetic to revolutionary elements or not.