1. The duty to go on a pilgrimage to the Temple (when it existed):

Three times a year shall you celebrate… the Festival of Ingathering…
Exodus 23:14, 16, 17

(The Hebrew word used here for 'celebrate' implies sacrifices which could only be brought at the Temple.)

2. The duty to 'appear'.

Three times a year all your males shall appear before the Lord your G-d at a place which He will choose: on the Festival of Matzot, and on the Festival of Shavuot, and on the Festival of Succot.
Deuteronomy 16:16

3. The duty to live in the succah.

Seven days shall you dwell in shelters (succot) .
Note: the word to 'dwell', does not imply a temporary stay, but something of a permanent nature. (In connection with a succah, the Hebrew "leshev" does not mean 'sit'.)
All the seven days one should make his succah his fixed home, and his house temporary. (i.e. used only for short periods)
Talmud Succah 28b

4. The duty to take the lulav (and its related symbols).

On the first day you shall take the fruit if a fine tree, branches of palms, the branch of a thick tree and willows of the brook.
Leviticus 23:40

5. Holy assembly and rest from specific activities.

On the first day, a holy assembly, you shall not produce any items of melachah (service).
Leviticus 23:35

6. The additional sacrifices.

A total of seventy bulls, fourteen rams, ninety- eight lambs and seven goats in the course of the seven days.
Numbers 29:12-34

7. The duty to enjoy the festival and be happy:

And you shall rejoice before G-d…
Leviticus 23:40
And you shall rejoice on your festival.
Deuteronomy 16:14
And you shall just rejoice.
Deuteronomy 16:15

7. The duty of celebrating with aravot (willows).

In the Temple, all seven days willows were laid on the side of the altar, with their tops overlapping onto the altar once, singing the Hoshanot:
Please, G-d, save us, please; please, G-d, grant us success, please!
Psalm 118:25

The Prophets established the custom of taking the willow on the seventh day and beating it, everywhere (i.e. not just in the Temple), as a reminder of the Temple.

8. Every olah or shelamim (offerings), whether obligatory or voluntary, private or public, had to be accompanied by a minchah offering of solet (a type of coarse flour) mixed with oil, and a libation of wine that was poured onto the altar.

On Succot the libation of wine was accompanied also by a libation of water. This law, not written down in the Torah, is traditional from the time of Moses.

9. Hoshanot: The modern custom is to circle the central platform (bimah) in the synagogue with the 'four species' saying the Hoshana prayers.

10. On the seventh day, Hoshanah Rabbah , we circle the bimah with the arba'ah minim seven times.

11. On the night of Hoshanah Rabbah , it is customary to wear white clothes and to spend the night reading the entire book of Deuteronomy and the entire book of Psalms.

12. On the morning of Hoshanah Rabbah , it is customary, when reaching a certain point in the Hoshana prayers, to put down the arba'ah minim and pick up, instead, a tied bunch of five willow branches (aravot); then to continue with prayers for water, and to shake the bunch of willows then beat them five times on the ground, in joy.

13. On this, the seventh and last day of Succot, in the late afternoon before it gets dark, it is customary to enter the succah and eat something, in order to observe the duty for the last time. On leaving the succah we say,

May it be your will that just as I was privileged to live in the shelter, so may I be privileged to live in the shelter of the hide of the hide of Leviathan.

14. It is customary to read Megillat Kohelet (the Scroll of Ecclesiastes) on Shabbat Chol Hamo'ed - the intermediate Sabbath of Succot. (If there is no intermediate Sabbath, then it is read onthe first day of Succot in Israel.)

Kohelet gives a warning that the enjoyment of the festival should be a Mitzvah in accordance with:

and I praised enjoyment
Ecclesiastes 8:15,
rather than the enjoyment that is not of mitzvah as in:
What good is enjoyment?
Ecclesiastes 2:2

16. Hak'hel At the end of the Shemittah Sabbatical Year, there is a public reading of the Torah before the entire population. Deuteronomy 31:10-13