By merely taking the four species and lifting them, one fulfills the mitzva, as it is written: “You shall take the fruit of a hadar tree…” (Vayikra 23:40). The Sages ordained shaking the lulav in the way that the Torah commands the waving of certain offerings (Sukka 42a; Menaḥot 61a).
The Gemara describes how the offerings were waved: “One moves forth and back, up and down.” That is, one moves the lulav away from himself and then brings it back, lifts it up and brings it back down. This is also an expression of faith: “forth and back – for the sake of the One to Whom the four corners of the earth belong; up and down – for the sake of the One to Whom heaven and earth belong (Sukka 37b). This is why the custom is to wave the lulav toward all four directions plus up and down. Our Sages further expound: “forth and back – to halt harmful winds; up and down – to halt harmful dew” (ibid.).
Additionally, following Rosh Ha-shana and Yom Kippur, the days of judgment when we stood before God in prayer, we begin the new year joyously. We wave the four species as a symbol of our victory in successfully repenting and renewing our close relationship to God (Vayikra Rabba 30:2; above, 1:3).
The procedure for shaking the four species is as follows: The bundled species in the right hand and the etrog in the left are brought together and held close to the body. Some are careful to pull them all the way to the chest. From there, the lulav and etrog are moved in a given direction, with the top of the lulav pointing upward but angled toward that direction. Then the four species are brought back to the body. This is repeated three times for each of the six directions (east, west, north, south, up, down). When shaking the lulav in the downward direction, one does not turn it upside down; rather, the top continues to point upward, and the person moves the lulav downward from the chest.
Some begin by shaking eastward and then continue moving rightward – south, west, north – and then upward and downward (SA 651:10). Some follow this order but begin with the direction that worshippers are facing.
According to the custom of Arizal, the first shake is to the south, followed by north, east, up, down, and west.
Some turn their whole bodies in the direction in which they are shaking the lulav; when they shake it upward and downward, they face east. Others face east the whole time but angle the lulav according to the procedure for shaking. All of these customs are acceptable, and each person should continue his family’s custom. If the custom is unclear, he may do as he wishes.
Ashkenazic custom is to shake the lulav such that its upper leaves rustle (MB 651:47). Sephardim do not follow this practice.