The four species are all requisite; if one of them is missing, the mitzva is not fulfilled with the other three (Menaḥot 27a). The mitzva is to take the four species together. Be-di’avad, the mitzva is fulfilled, and the berakha may be recited, by taking them serially (SA 651:12).
Not only is there a mitzva to take all four species together, there is also a mitzva to bundle the lulav with the hadasim and aravot, as doing so beautifies the mitzva, and beautifying a mitzva is itself a mitzva, as the Torah says, “This is my God and I will glorify Him” (Shemot 15:2). But the etrog is not bundled with the other three. The Sages derive this from a subtlety in the verse (Vayikra 23:40) that describes the four species. The lulav, hadasim, and aravot are joined by a conjunction, the letter “vav,” while the etrog stands alone (“pri etz hadar, kapot temarim va-anaf etz avot ve-arvei naḥal”). Thus, the etrog is not bundled with the rest.
Some say it is necessary to use a permanent knot – the kind forbidden to tie on Shabbat, like a double knot. Consequently, even those who use koishelakh (“little baskets” woven from lulav leaves) to hold the three species together should also bind them with a double knot (SA 651:1). Others say this is not necessary; rather, the main thing is for the three species to be bundled together (Ritva; see MB 651:8).
Despite the fact that many people bundle the three species using lulav leaves, one may use any type of thread or strap (SA 651:1).
When bundling the lulav with the hadasim and aravot, one must make sure that the spine of the lulav extends at least a tefaḥ beyond them (SA 650:2). If the hadasim and aravot are long and the lulav is so short that its spine does not extend a tefaḥ beyond them, one must either shorten the hadasim and aravot to the minimum requisite length of 3 tefaḥim, so that the spine of the lulav extends a tefaḥ beyond them, or one should bundle them lower than the lulav, so that the spine of the lulav extends a tefaḥ beyond their tips.
One should not take more than one lulav and one etrog at once. The minimum is three hadasim and two aravot, and if one wishes to add hadasim and aravot he may, although many are meticulous not to add to the required three hadasim and two aravot (SA 651:15).
One may not add a fifth species to the four mandated by the Torah. One who does so violates the prohibition of “bal tosif” (adding mitzvot to the Torah) (SA 651:14).
Some place the hadasim on the right of the spine of lulav and the aravot on the left (Shlah; MB 651:12). Others place one hadas on the right, one on the left, and one in the middle, and one arava on the right and one on the left (MA ad loc. 4 in the name of Arizal). Both ways fulfill the mitzva even for the most meticulous.
Some are meticulous to have the hadasim extend a little higher than the aravot, because hadasim symbolize the righteous, while aravot allude to the unlearned (Rema 651:1).
In addition to the mitzva of bundling the three species together, some are meticulous to bind the lulav itself with three additional knots, though Ashkenazim take care to leave the top of the lulav unbound, so that it rustles when shaken (Rema 651:1; MB ad loc. 14). Some have the custom of binding the lulav with 18 knots. (See Kaf Ha-ḥayim ad loc. 16.)