what's the fastest way to increase obedience?
Take them onto the streets, chat, kiss and hug until joy is high enough above stress, then french kiss. This works so well there's enough turns left over to take them to the garden for a few teaching sessions. That's assuming Obedience isn't capped by rebelliousness or Uncivilized trait. The fastest way to remove rebelliousness is an amnesia potion, the fastest way to remove Uncivilized is an elixir of regression.
Other ways to remove rebellion is Fear, Domination and Summon Tentacles spells, or taking them down to the dungeon for good old fashioned torture. With these methods, rebellion won't be completely cleared until the morning after rebellion strength drops to 0.
The only other way to remove Uncivilized is with a Tamer specialist, but this is far from the fastest. If you don't have Ayneris' shop unlocked to buy elixirs, then the torchable caches in the Elven Grove have a decent drop rate for them.