I remember it as the parent holding the child's outstretched arm, palm upwards, doing round and round the garden with her/his fingers on the palm and then running the fingers up the arm to the armpit and Tickle you under there! - happy days!
I was reading somewhere when googling this that it is done on a child's tummy. I never remember that. It was always done on the upturned palm of a childs hand a far as I know!!