According to the Shulhan 'Arukh, when shaking the Lulab, one should move towards the right, going East, South, West and North. The Mishnah Berurah writes that this is the common custom in Ashkenazi lands. Moving to the right applies irrespective of whether one is right handed or left handed.
He writes further, that it is not necessary to turn one's face to the direction that one is pointing the Lulab in, but that it is sufficient to point the Lulab in that direction, doing it over one's shoulder when pointing West. The custom according to the Ari, z"l, is different, however.
His order of shaking, which is followed by Sephardim and those who shake the Lulab according to the Sod (Kabbalistic teachings), is to shake the Lulab in the following directions: South, North, East, Up, Down, West. In this case, one turns one's whole body to face the direction the Lulab is pointing in. When saying the Berakha (blessing), however, one should face East.
(See Shulhan 'Arukh, 651:10. Mishnah Berurah, ibid., 47. Kaf Hahayyim, ibid., Oth 96, 103. Yafeh Laleb, ibid., 10)
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