As Dante enters the second circle of hell, that of the Lustful, he is witnessing the first real punishments of the Inferno, since the first circle, Limbo, has no suffering for the virtuous pagans. At the edge of the second circle stands Minos, the semi-bestial judge of the damned, whom Dante modeled after one of the judges of the dead in Hades from classical mythology. Minos’ job is to judge and assign sinners to their deserved levels.
In Dante’s conceptualization, sinners have chosen their immoral behavior, therefore they are strangely eager to cross the river Archeron and face their judge. “There Minos stands, / Grinning with ghastly feature: he, of all / Who enter, strict examining the crimes, / Give sentence, and dismisses them beneath.” Basically, as they stand before Minos, they are forced to fully confess their sins, and they cannot lie, since Minos can discern truth from lies anyway.
The creature then determines which level of hell each soul deserves: level one for the lighter sins of incontinence, level two for the sins of violence, or level three for the sins of fraud. Minos also selects the appropriate circle within each level, according to the sinner’s specific sins. "[A]nd that judge severe / Of sins, considering what place in Hell / Suits the transgression, with his tail so oft / Himself encircles, as degrees beneath / He dooms it to descend... / Each one to judgement passing, speaks, and hears / His fate, thence downward to his dwelling hurl’d.”
In plain terms, upon determining the sins of the soul before him, Minos wraps his whip-like tail around himself the same number of times that equal the sinner’s deserved circle. So to demonstrate, a sinner who had committed crimes of extreme anger during life would watch in horror as Minos encircled himself with his tail five times (for circle five, that of the Wrathful).
Dante never explains exactly how the souls get to their circles, simply that each is “downward to his dwelling hurl’d”. Considering that the Florentine poet’s purpose in writing the Inferno was to warn the unrepentant to change their ways, it is perhaps more effective that he doesn’t give us all the details. Sometimes our imaginations are more capable of horrifying us.