Increasing xp gain and leveling up champion faster?

Hello, Im a fairly new LoL player, and I have a few questions about the leveling system when it come to your champion. It seems that even if I have the most cs in the whole game out of everyone, and even have gotten a couple kills, Im still 1/2 levels behind. Im just very confused on the system, and I was hoping someone could help me out, and maybe give a few tips for leveling up your champion in a game. Thanks alot!