Lately it's been the "Coyote Method".
Not deliberately, of course. Either hawks or coyotes (not sure; we're in the process of setting up cameras) have taken several of our flock. We're still figuring out what to do about it.
We've tried the broomstick method but it's hard. What works best for us is to take a traffic cone, cut off the top of it, mount it upside down, stuff the chicken in it so their head is poking out the bottom, and slit their throat with a very sharp knife. It's gruesome and if your family is squeamish it won't go well. But they go quick and drain out, so cleaning is easier.