/cast [target=party1target, exists, dead] Skinning

You have to update the macro when your skinning skill advances.

So it becomes:

/cast [target=party1target, exists, dead] Skinning(Expert)
/cast [target=party1target, exists, dead] Skinning(Artisan)

Target the dead thing you want to skin on your main and hit the macro. If your skinner is close enough he will skin it. Also helps to turn on Auto-loot.

This should get put in one of the sticky threads I've posted this macro a bunch of times.