The accepted practice when washing Netilat Yadayim in the morning is to pour water on each hand three times, in alternating fashion. Meaning, one first pours water on the right hand, then the left, a second time on the right, a second time on the left, and then a third time on the right and then the left. The Seder Ha'yom (Rav Moshe Ben Machir, Sefat, 16th century) maintained that one should pour three times consecutively on the right hand, and then three times consecutively on the left hand. Due to the difference of opinion, there were those who washed their hand twice, once in each sequence, in order to satisfy both views. However, the Kaf Ha'haim (Rav Yaakob Haim Sofer, Baghdad-Israel, 1870-1939) writes that the Arizal taught that one should wash in alternating fashion, and this is the accepted practice.
The Zohar explains that each hand must be washed three times because the impurity that descends upon the hands during the night is particularly difficult to remove. It has a way of "jumping" from one hand to the next, and the only way to remove it is by causing it to "tire," so-to-speak. We therefore wash three times in alternating fashion to eliminate this impurity.
It is proper to use a copious amount of water for Netilat Yadayim, to ensure that water covers the entire hand with each pouring.
Maran (Rav Yosef Karo, author of the Shulhan Aruch), in Bet Yosef, notes a seeming contradiction between two passages in the Zohar regarding Netilat Yadayim. In Parashat Vayesheb, the Zohar writes that one first washes the right hand, before washing the left, and this is, indeed, the accepted practice, as mentioned. Elsewhere, however, in Parashat Teruma, the Zohar instructs washing the left hand first. The Bet Yosef initially suggests reconciling these two passages by distinguishing between the washing in the morning, and the washing before eating bread. In the morning, when we seek to eliminate the Tum'a (impurity) from the hands, it would be improper to begin with the left, as the forces of Tum'a are associated with the left – which is the side of Din, judgment – and giving it precedence would have the effect of empowering those forces. We therefore begin with the right, the side associated with Hesed (kindness). When washing for bread, however, the Zohar instructs starting with the left hand.
But the Bet Yosef then presents a different way to reconcile the two passages in the Zohar, which he felt was more correct, and according to which one begins with the right hand for both the morning washing and Netilat Yadayim before eating bread. He explains that in Parashat Teruma, the Zohar refers to washing, but to lifting the cup, and teaches that one should not pick up the cup with the left hand. Instead, one should pick up the cup with the right hand, and then transfer it to the left, as though asking the left to serve the right, thus showing that the left side – the side of Din – is subservient to the right side, the side of Hesed. But as for the actual washing, one always begins by pouring water from the left hand onto the right hand.
This sequence should be followed even by those who are lefthanded. Precedence is given to the right hand when washing Netilat Yadayim not because of the right hand's dominance – in which case we might distinguish between righthanded individuals and lefthanded individuals – but rather because of the association between the right and Hesed. This association is true regardless of whether one is righthanded or lefthanded, and so even a lefthanded person begins with the right hand when washing Netilat Yadayim.
The Mishna Berura brings the opinion of the Gaon of Vilna (1720-1797) that one should wash both hands a fourth time. The Gaon maintained that the water that remains on the hands after the third washing contains impurity, and thus it should be washed off the hands. Many people follow this practice. The Yalkut Yosef writes that if one does not follow this practice, he should ensure not to touch his face with hands after the morning washing until his hands are dry.
As mentioned, one should always lift the cup with his right hand and then transfer it to the left, in order to express the left's subservience to the right. One must avoid transferring the cup directly from the left hand to the right hand, as this would suggest the right's subservience to the left. Therefore, after one washes his right hand with the cup held by the left hand, he should not transfer the cup directly to the right hand, but should instead put it down, and then lift it with the right hand.
The proper procedure, then, is to lift the cup with one's right hand, transfer it to the left, pour onto the right, place the cup down, lift it with the right, pour on the left, and then transfer to the left for the next washing. Of course, this should then be repeated a third time (and a fourth for those who wish to follow the Gaon of Vilna's practice.)
The Seder Ha'yom maintained that while washing Netilat Yadayim, one must ensure not to touch a moist part of the cup's handle, as this would contaminate those drops of water, which will then contaminate the other hand. The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909), however, disagreed. He explained that according to the Arizal, the forces of impurity do not affect a small, negligible amount of moisture, such as the droplets on the handle of a cup. Therefore, while washing Netilat Yadayim, one can touch any part of the handle.
It is not necessary to use a cup with handles for Netilat Yadayim. Such a cup offers the benefit of helping to ensure that the hands do not touch each other during the process of transferring to the cup, but it is not required, as long as one sees to it that his hands do not touch.
Summary: When washing Netilat Yadayim in the morning, one must wash his hands three times in alternating fashion. The proper procedure is to lift the cup with one's right hand, transfer it to the left, pour onto the right, place the cup down, lift it with the right, pour on the left, and then transfer to the left for the second washing. This should then be repeated a third time. Some then wash both hands a fourth time. Those who do not should ensure not to touch their face after Netilat Yadayim until their hands are dry. This procedure should be followed by both righthanded individuals and lefthanded individuals. It is proper to use a copious amount of water for Netilat Yadayim, to ensure that water covers the entire hand with each pouring.