When taunting I just hit the boss with something that hits hard like a Shield of the Righteous or Avenger's Shield on my Paladin, or Shield Slam/Revenge on my Warrior. Whatever I taunt tends to stick to me after doing that.
At present, for the duration of your taut's fixate (3 seconds) any damage dealt to that target has it's threat increased (to the tune of 21x Damage dealt) so making sure you have some hard hitting abilities is always good. However the first taunt swap is probably the most dangerous as threat levels are low and it's easy for me to over aggro the other tank, so if i know i out gear the other tank, or can't let up on my rotation for even a few seconds to give them breathing room generally HoS myself when the other tank taunts off me (or briefly swap to Battle stance, Tiger stance or Unholy Presence, or cancel Righteous Fury), just to give them an easier job of keeping aggro.
Taunt swapping is about co-ordinating you threat, you shouldn't really be fighting the other tank for it, especially not for the sake of epeening over ones DPS.