Perception is neither a skill nor an attribute, so you cannot "level" it in any way.
It is mere a concept that can be in two different states: Rushed or Careful.
The player has to announce how he/she is doing something. The DM might ask about it if the player forgets to announce it.
If a player is rushed, the rushed action is done quicker. The player sacrifices attention to detail or accuracy for time.
Example: The player is in a dungeon and the path ahead splits. The player announces, that he quickly checks out which way to go because he fears a monster attack. The DM tells the player only superficial information, that it appears that there are more footsteps going into the left tunnel. The player decided to go left and walks into a room full of monsters. After killing them all, barely alive, the player finds a treasure chest but no way to the outside.
If a player is careful, the careful action takes more time because the player is paying more attention to detail.
Example: The player is in a dungeon and the path ahead splits. The player announces, that he carefully checks out which way to go. The DM tells him that it appears that there are more footsteps going into the left tunnel, but looking closer it seems like the footsteps that go into the other tunnel were wiped away, seemingly on purpose. Because the player took some time for this observation, he gets ambushed by a monster. After defeating it, the player goes to the right tunnel that eventually leads to the outside.