After the player triggers the explosion of the Sigil Geode near the start of the quest Something Strange, they can begin to find things around Skyrim possessed by Spirits.
Items, furniture, creatures, and enemies can be found throughout the world or in dungeons with a light blue glow on them.
Interacting or hitting any of these things (with the exception of enemies) will trigger the Spirit to leave its vessel and attack the player. For enemies, the Spirit will instead remain in the host until after it's killed, at which point it will vacate the corpse and attack the player.
These Spirits are guaranteed to have Ectoplasm, and if the player finishes them off with the Seance spell unlocked during the unmarked side quest The Friend, they will gain additional Ectoplasm.
Possession can happen nearly anywhere, inside of dungeons, and out in the world.
After the player completes the quest Something Strange, the player will learn of Ghost Hunts, which can help them find clusters of these possessions occurring.