It's never easy...first time is definitely the hardest.
First time I slit a jugular to slaughter a bird for meat,
the stress adrenaline about knocked me off my feet,
and took a good 30 minutes to recede.
I use Cervical Dislocation to euthanize sick birds.
It took many hours to find a video using a broomstick where the head didn't come off.
Cervical Dislocation is shown in this video at about 1:00,
it's the only CD video I've found that doesn't remove the head.
Notice the slight divot in the ground under the stick and neck, this will keep the bird from being choked and struggling.
Notice that she slowly stretches out the neck and legs before giving the short sharp jerk that breaks the neck ,
this is key to success, IMO.
I've found this technique to be very effective.