The ranks go in this order: (worst to best)
Dirt
Coal
Cobblestone
Iron
Gold
Diamond
Obsidian
The more games you play, the better your rank will get, if you are winning the games. The quicker you win the game, the more points you will earn; however, that does not affect your rank. What affects your rank are your statistics that you get while playing the game. Some statistics that affect your rank are Bystanders Shot, Overall Win/Loss Ratio, Murderer Win/Loss Ratio, Bystander Win/Loss Ratio, and several other stats. Achievements and Upgrades do not affect your rank.
So Basically, every time you stay alive in a game, your rank goes up higher. Shooting innocents makes it dramatically drop, so don't shoot unless you are 100% positive that the guy is the murderer. If you are the murderer, your rank will go up if you successfully kill everyone else. If you are bystander, your rank will go up if you are alive when the game ends, and even higher if you shoot the murderer. So, Good Luck to you!