A golden plus in the left upper corner of character portrait informs you about gaining new level.
Pillars of Eternity has a specific system of gaining experience. Its most important aspect is the lack of experience for defeating enemies (the only exception is if killing a monster has earned you a new entry in the bestiary - these types of actions are awarded with xp). A won duel gives you only new items and pushes the storyline further. Experience is given to the whole team, not specific members. It means that a team with less members will gain experience faster than a team with more of them. Four most important sources of experience are:
Quests - you will get most experience for completing main story quests, but without completing side quests you won't develop your character to max level. With a party of 6 characters main quest will allow you to get no further than to 8 experience level.
As in every RPG, experience is the key to character development in Pillars of Eternity.
World exploration - for entering a new location (including some buildings and caves) you will get a small amount of experience.
Interacting with the world - experience is given for disarming traps, opening chests and any other form of interaction with the game world.
Experience showing in the combat window is not given for defeating enemy but filling the bestiary.
Updating the bestiary - you receive small amount of experience for few first fights with a specific monster type. It is given for unveiling enemy stats. How fast you reveal it depends on lore level of your character. You don't receive experience for the battle itself.