Although the essence of the obligation is fulfilled by simply "taking" the four species into one's hand, the preferred method of fulfilling the mitzvah is to wave the lulav three times in all six directions [forward, to the right, to the back, to the left, up, and down].
The Talmud offers the following explanation for this practice: It is as if he is taking them [the species] and bringing them to Him Who owns the four directions. He raises them and lowers them to Him Who owns the heavens and the earth (Sukkah 37b).
The four species, and all that is connected to them, are an allusion to G-d's creation of all that is, and that there is none besides Him. The Sages (ibid.) also said: He takes and brings them [i.e., waves them in all directions) to restrain the harmful winds. He raises them and lowers them to prevent harmful dew.
Sukkot is the time of year when the world is judged regarding the amount of rain which will fall for the entire year. The "taking" of the four species gives symbolic expression to our prayers for the blessing of water.
The etrog needs more water than do other fruit trees, palm branches grow in valleys which are well-watered, and myrtles and willows grow near water. In waving the four species in all six directions, we therefore symbolically declare to Him Who sustains the whole world: Just as these four species cannot exist without water, so too can the world not exist without water. When You bless us with water, let no harmful winds or injurious dew undo Your blessing.
The na'anuim are performed when one recites the berachah upon taking the four species, and four times within the recitation of Hallel.
There are two accepted customs regarding the order of the na'anuim. One tradition is to wave the species to the front, to the right, to the back, to the left, up and then down. The other tradition is to wave the species to the right, to the left, to the front, then up, down, and to the back.
Click here for an illustrated diagram of how to perform the na'anuim (movements) with the Lulav and Esrog
