All ranked matches use default VS rules (80 seconds per round, first to win 2 rounds wins the match) and cannot be adjusted. (Player matches can change the time limit and # of rounds, but these options are still more limited than what is available in local play.)
There are four separate stats that are kept track of in ranking mode: number of wins/losses, score, experience points, and rank title.
Whenever you win a match, your score increases by 4 points regardless of either player's other stats. You also receive 1 point when you lose, so there is no incentive to drop from a match. If you do drop a match or are disconnected, you will receive a loss with no points added to your score. I am not sure what happens if a game ends in a draw. The ranking mode leaderboard is based purely on score, so if you want to aim for the top quickly, beating up on low skill opponents is the fasted method.
You receive a specific number of experience points whenever you win a match. Defeating a player with the same rank title as you will give you 20 EXP. Defeating a player one rank higher will give you 21 EXP, two ranks higher 22 EXP, etc. Defeating a player one rank lower gives you 10 EXP, two ranks lower 9 EXP, etc. I think you are always guaranteed at least 1 EXP even if you defeat someone of much lower rank. You do not receive any EXP from a loss. The fastest way to gain EXP quickly is to only challenge players with a rank equal to or greater than your own. Some other players will in fact only accept challengers of equal rank or greater, so challenging only those equal in rank to your own slightly decreases the odds of the other player refusing your challenge.
After earning a specific amount of EXP, your rank title increases to the next level, with increasing amounts of EXP required to advance further. Since there doesn't seem to be any numeric representation of your total EXP (only a visual bar that fills slightly with each victory), it's difficult to determine exactly how much is required for each rank. Below is a crude visual representation for each rank title I'm aware of.






















































































Feel free to make any additions or corrections to this info.