For this answer, I'll mostly be working from Maester Baelgar's A Trade in Flesh. I'm well aware of his tendency to conflate myth and reality, particularly with regards to the so-called "Children of the Forest", but the only copies of many of the works that he himself alludes to were lost in the Sack of King's Landing in 283 AC, leaving modern historians to rely upon Baelgar's commentaries or forgo discussion of the topic at all.
Little is known about the social economy of the First Men of Westeros. The vast majority of runic inscriptions from that era are still untranslated, and those that have been are mostly centred around recording feats of conquest and personal heroism by male aristocratic patrons rather than the everyday lives of the peasantry and of women. There are a number of very suggestive pictographs chiseled into the walls of the excavated ruins at Crackclaw, but little more.
Archaeological excavations of the Barrowton necropolis complex provide some of our best material evidence for the practice. Among the grave goods there have been found a number of engraved gold and silver plates depicting tribal leaders surrounded by smaller female figures - presumed to be concubines. Many of the carvings dismissed as "primitive fertility goddesses" by the prudish Maesters of a century or two ago have since been re-interpreted as likenesses of individual courtesans, buried as a sign of favour with particular patrons.
Another interesting, if under-documented, instance of prostitution among the First Men can be found in the records of the temples dedicated to the Lady of the Waves. Travelers such as the eunuch Hazzar bin-Hazzar went into some detail on a ceremony that was still performed once per lunar year well into the Andal Era. In celebration of the mating of the Lady of the Waves with the Lord of the Sky, priestesses would go among the people and engage in some (graphically described) sexual rituals in exchange for a donation to the temple.
We can infer from the pieces of material culture that survive from the period that brothels were illegal across many parts of the continent, but the law was either rarely enforced or simply flouted. And, as always, it's important to bear in mind that contrary to the pop-culture interpretation, the First Men were not a monolithic society; each tribal group, while sharing many social characteristics with their fellows, had their own customs and traditions. Some would naturally be more lax with regards to sexual mores than others.