Sabbahillel, you write that
"While wrapping one’s self in the talis it should be pulled down to one’s mouth and the tzitzis should be thrown over one’s left shoulder"
Aruch Hashulchan (siman 8, para 8) explains that the initial wrapping around the head is done to satisfy the halachic opinion requiring Atifas Yishme'elim (Arab style headdress).
As such, I have seen other Seforim critique the manner of atifah that you quote described above "pulled DOWN to ones mouth". This is patently not how Arabs wear head coverings! Instead, they suggest (as per the Aruch H) it refers to the part of the Tallis thrown over the (left) shoulder, which should cover " UP to the upper lip", and as such closely resembles Arab style headdress.
To summarise, the top part of the Tallis covers the forehead, the lower part is bunched together and thrown over the left shoulder thereby concealing the mouth, and held in position for "hiluch arba Amos" (approx 5 seconds), to fulfil the opinion requiring atifas yishme'elim.