Hacham Ovadia Yosef, in his work Hazon Ovadia – Laws of Sukkot (p. 352; listen to audio for precise citation), writes that when fulfilling the Misva of Lulav, one holds the Lulav with the Hadasim and Aravot in his right hand, and the Etrog in his left. This applies even to those who are left-handed. Throughout the performance of the Misva, including during the Ni'anu'im (waving), the Lulav and Etrog must be held together such that they touch each other.
Our practice regarding waving the Lulav follows the position of the Arizal (Rabbi Yishak Luria, Israel, 1534-1572), who held that one waves in the following sequence: south, north, east, up, down and west. When changing directions, one should always turn towards the right until he faces the proper direction.
The Lulav is waved during the recitation of a number of verses in the Hallel service, including the verse "Ana Hashem Hoshi'ana." Hacham Ovadia writes (ibid. p. 355) that while one waves the Lulav as he recites the word "Hoshi'ana," he must ensure to recite the word in a single breath. If he takes a breath in the middle of the word, the word loses its meaning. Hence, even though one must prolong the recitation of this word to complete the Ni'anu'im, he must ensure not to interrupt with a breath. Hacham Ovadia rules that it is preferable to hasten the Ni'anu'im rather than take a breath in the middle of this word. If a person is short of breath and cannot complete the Ni'anu'im while reciting "Hoshi'ana" unless he takes a breath, then he should wait to wave the Lulav until after reciting this word.
At no point should a person wave the Lulav while reciting God's Name.
It is a Misva for women to take the Lulav and Etrog, despite the fact that, according to our practice, they do not recite the Beracha. Hacham Ovadia writes that it suffices for women to simply hold the Lulav and Etrog; they need not perform the Ni'anu'im. He cites this ruling in the name of the Ben Ish Hai (Rabbi Yosef Haim of Baghdad, 1833-1909).
On page 376, Hacham Ovadia mentions the practice advocated in a number of works (Sha'ar Ha'kavanot, Nagid U'mesaveh, and Birke Yosef) to take the Lulav in one's Sukka at sunrise, the earliest time when one may perform this Misva. (It should be noted, however, that one who took the Lulav before sunrise has nevertheless fulfilled his obligation, provided that he did so after Alot Ha'shahar – daybreak.) Adherents of this custom recite the morning Berachot and then go into the Sukka to take the four species and perform the Ni'anu'im. They then take the four species to the synagogue so that they can perform the Ni'anu'im during the Hallel recitation, but they do not repeat the Beracha over the Lulav, since they had already fulfilled their obligation. One who does not have a Sukka at home but wishes to follow this practice can take his Lulav and Etrog in the synagogue's Sukka before the morning Shaharit service. (As mentioned, one should recite the Birkot Ha'shahar – the morning blessings – before taking the four species.)
It is a laudable practice for men to immerse in a Mikveh on Erev Yom Tov. When the Bet Ha'mikdash stood, people had to immerse themselves before the onset of the festival because they would have to offer sacrifices in the Temple. It is thus proper to commemorate this practice by immersing in a Mikveh on Erev Yom Tov.
