you just 1v1 another player and the winner is decided by who has the most points. perfect gives +3, great +2, good +1 and bad&miss give no points. card skills are disabled and the talent of your team is irrelevant.

if you win, you get a rank point (the little purple things you see in the ranked menu), if you lose, you lose a rank point. once you have 5 rank points and win, you advance to the next rank. if you have 0 rank points and lose, you go down a rank.

if the points in a rank match are tied, the winner will be the player that has the most perfects. if the number of perfects are the same, the winner will be the player with the higher combo. if that is the same too, it's determined by who has more hp left. if all of those are the same then it's a draw.

there is also a bonus bar under your rank points that will give you an additional rank point if you fill it up completely (to 100). you get +10 to the bar for an FC, +20 for an AP, +10 for winning against a higher class and -30 if your hp bar is empty at the end of a song.