Defeat as many monsters as you can. Fight monsters that give you the maximum experience points (Exp, XP, measure of character progression) and try not to die. By accumulating these points character increases in level.
XP are not displayed in the game, but  in the character's information in tab Skills you can see what percentage of experience you need to reach the next level.
Defeating monsters is the primary way to earn XP, but also you can earn XP by completing quests.