For Hosha’anos, a Torah is held at the Bimah by someone who does not have a set of Daled Minim (or someone in the year of Aveilus who doesn’t circle the Bimah). If all have a set, the Torah is placed on the Bimah. The Aron Hakoidesh remains open throughout Hosha’anos.
When reciting the Hosha’anos unique to that day, the initial phrases are recited quietly at one’s place, each phrase being preceded with the word Hosha’anah. The phrases from the letter “Samech” or “Ayin” onwards are recited aloud after the Chazzan, with each phrase preceded and followed with the word Hosha’anah. These phrases are timed to coincide with one complete circuit around the Bimah.
During Hosha’anos, the Lulav is held with the right hand and the Esrog with the left. The Rebbe would generally hold them joined together and touching his chest.
One without Daled Minim does not circle the Bimah. [It is best to borrow a set in order to participate.]
The last Posuk (i.e. L’Maan Da’as) is said aloud when the Sefer Torah is returned to the Aron Hakoidesh. One holds the Daled Minim until this time.
One who is davening without a Minyan should still circle the Bimah. If at home where there is no Bimah, one should still circle a table. (Some maintain that a Sefer should be placed on the table.)
On Yom Tov, one may return the Lulav to the moist towel or water that it was already in. One may also place it in another moist towel or other water, as long as they were prepared before Yom Tov. One may add water to either of these, but may not completely change the water.