The animal must be slaughtered by the use of a sharp knife. The knife must not kill due to its weight. If it kills due to the impact the meat may not be permissible.
The windpipe (throat), food-tract (oesophagus) and the two jugular veins must be cut.
The slaughtering must be done in one stroke without lifting the knife. The knife should not be placed and lifted when slaughtering the animal.
The knife should be hidden from the animal, and slaughtering should be done out of sight of other animals waiting to be slaughtered.This sounds virtually identical to kosher slaughter (although kosher slaughter requires a much longer knife to ensure that the animal is killed swiftly.)
Animals should be killed in a comfortable way. Unnecessary suffering to them must be avoided.
But as many videos from Eid al Adha show (this one from Gaza,) the requirement of a single stroke is almost never done, at least in front of the crowds recording the slaughter.
(Warning: this is horrific to watch.)
The slaughterer does not even hold the blade so the sharp end severs the neck. Instead, he is stabbing the poor creature in the neck, repeatedly, to the cheers of the crowd watching it painfully die over the course of minutes - as the next animal watches and is clearly agitated when its turn comes up.
Forget PETA. Shouldn't religious Muslims themselves be upset over this fairly clear violation of Muslim law?