First and foremost, leveling in Dark and Darker works exactly as one would expect Dark And Darker Gold. As a character levels up, they gain access to previously locked mechanics/features. But, unlike other games, leveling up in DaD does not mean stats are increased, at least not yet. There's a Class Training tab in the game currently that's inaccessible.
Players speculate that this is where they'll be able to increase certain stats like Strength or Agility (depending on the best stats for their class) as they level up. This is where a lot of the 'build' diversity would come in that would make characters feel more individual. For example:Barbarians could build into either raw damage or pure tankiness.
Wizards could build for either Spell Cast Speed, Spell Damage, or somewhere in between. Rogues could spec into raw Agility for quick looting or Strength for more damage per stab. Of course, this is all hypothetical because again, at the moment, all leveling does is give players access to more Perk Slots, with 1 by default, 2 at level 5, 3 at level 10, and 4 at level 15. Other than that, there isn't any sort of 'numerical' reward for leveling, especially past level 15.
Now, with the general concepts understood, where do beginner Dark and Darker players go to gain EXP? Well, there are quite a few ways to go about this. The most obvious method is to get into the dungeon and kill NPC enemies or other players. But, there are a lot of other actions that grant EXP besides this. All of these actions grant EXP buying Dark And Darker Gold, and this likely clears up some questions players might have had about why someone in their party was leveling faster than they were.