We hold the lulab, the hadasim, and arabot in our right hand and the etrog in our left hand to perform the Mitzva of netilat lulab (see here ). When we hold the four species together, they must be held in the direction they grow on the tree (see video below).
Since every Mitzva has to be performed necessarily after we say the blessing, some people hold the Etrog upside down and turn it back after the blessing (otherwise the berakha will be said after the Mitzva is performed!). Others, hold the etrog in their left hand only after they said the berakha.
The Sephardic custom is not to 'shake' (rattle) the lulab (= in this context "lulab" means: the whole set of the four species) but to 'move it' (lena'anea) toward six different directions.
During the Halel, for example, we move the lulab clockwise: first South, then North, then East, then up, then down and finally West. This is done following the instructions of Chakhme haKabbala .
When waving it downward, we should not turn the lulab upside down, so that its head is facing downward, but simply moving it with our hands in the direction of the floor. We should turn our whole body as we face the direction to which we move the lulab.
We do not perform the Mitzva of lulab during Shabbat.
Women are formally exempted from the Mitzva of lulab. The tradition in most communities, however, is for women to take the lulab. Rabbis are divided on the issue of women reciting the berakha. In general, Sephardic Rabbis would oppose to the recitation of the berakha by women and Ashkenazi rabbis would approve.
Each person should follow his or her family's traditions.
Candle Lighting today in NYC: 6:02
DO NOT FORGET, before the holiday Erub Tabshilin