It depends on the size of the corpse. If you can pick it up without dragging it, I think you need to hold either left or right click and shake your mouse left and right quickly. If you cannot pick it up, you need to bite the corpse until you've opened it up enough to get the organs out. Once it has been opened up enough, you tap the G button (i think it was the G button..) to grab a piece of meat. If the corpse has been opened enough, and there are organs inside, you will get an organ. If you get a piece of meat instead, then you need to continue biting the corpse more (that or all the organs have already been pulled out).
