137:3 It is proper for one to remove his tefillin before taking the lulav, or at least to remove the strap around his hand so that it will not be a barrier between his hand and the lulav. It is also advisable to remove any rings one might have on his fingers.
137:4 The order of the waving the lulav in Hallel is as follows: In the phrase “hodu laShem ki tov, ki l’olam chasdo,” there are six words other than G-d’s Name. On each word, we wave in one of the directions; we do not wave while saying G-d’s Name. At “hodu,” we wave east, at “ki,” south; at “tov,” west; at “ki,” north; at “l’olam,” up; and at “chasdo,” down. The shaliach tzibbur only waves during the lines “hodu” and “yomar na Yisrael,” but the congregation waves every time they say the refrain of “hodu.” (When davening alone, he only waves when saying the one line of Hodu at the beginning – Mishnah Brurah 651:41.)
In “Ana Hashem,” the shaliach tzibbur and the congregation only wave for the first phrase, “ana Hashem, hoshia na.” Since there are three words apart from G-d’s Name, on each word we wave in two directions. At the “Hodu” at the end of Hallel, the shaliach tzibbur and the congregation both wave again. When waving downward, only the hand is lowered; the lulav and the other species remain pointing upward, in the direction that they grew. Some have the custom to turn the lulav downward and each person should follow his own practice. One does not need to turn his face in the direction he is waving, just the top of the lulav. One does not need to wave forcefully; it is sufficient just to shake it a little so that the leaves rustle.